Engine surging all speeds - VN 1500 Vulcan Classic kawasaki Motorcycles

Surging (governor hunting) at idle is usually a fouled carburetor.

Does it not surge when engine is operated at high speed?

If it is governor hunting at both at high and low speed, then either it has a vacuum leak (unlikely) or contaminated fuel especially when fuel has ethanol. Suggest you drain the fuel from tank(s)and the carburetor fuel bowl. Then try a couple gallons of fresh fuel from a station. Don't use what you may have on hand as it too may be contaminated.

If it only hunts at low speed then less likely it is a fuel problem and the carb low speed circuit has a blockage and will need cleaning.

There is also the possibility of a fault in the safety circuit that kills the engine when PTO enabled but with the governor hunting it's likely a carburetor issue.

Is the car equipped with the Automatic Transmission?
If so, read on.
Otherwise skip to the end and answer some questions.

POSSIBLE SCENARIO:
I have observed a condition where my car surges slightly when the torque-converter clutch (TCC) cycles between lock and unlock when driving on an uphill grade.
First some basics and history that will explain why the TCC is used.

Engine, Torque Converter, TCC, and Transmission relationship--
The TCC allows for a solid connection between the engine and transmission which allows the input to the transmission to rotate at the same speed as the engine.
Without a TCC, there is slippage between the engine and automatic transmission. The slippage is greatest at low engine RPM. That is what allows the engine to run with the automatic transmission in gear, like when you first shift into gear or stop at a stop sign. When the throttle pedal is depressed, the engine RPM begins to increase and the torque converter begins to slip less and less the more the engine RPM increases. The car moves. But even at cruising speeds the torque converter slips slightly. Engine RPM is greater than transmission input RPM, which is realized as slight decrease in fuel efficiency.
When acceleration is complete and a constant speed is being maintained, the engine power output is reduced to the point where the TCC can engage and eliminate any slippage between the engine and transmission. If the car has a tachometer the engagement of the TCC can be verified when a slight reduction in engine RPM observed without a corresponding change in vehicle speed.
One method used to test the operation of the TCC is as follows:
Find a flat section of road where it is safe to perform the test.
Reach a steady speed and keep the gas pedal depressed with one foot. While observing the tachometer (or listening for an increase in engine RPM), with the other foot depress the brake pedal enough to activate the break light switch but not enough to engage the brakes. When the brake light switch activates, the TCC receives a signal to disengage. With the gas pedal being held steady, release the brake pedal and the engine RPM should decrease when the TCC engages.
Old cars with Automatic Transmissions did not use a TCC. I believe the TCC was put in use in an attempt to increase fuel economy.

MY EXPERIENCE WITH SIMILAR SYMPTOMS
The condition that causes that issue on my car is this:
- A slight uphill grade increases the load on the engine.
The car tends to gradually slow and it is necessary to depress the gas pedal to maintain speed.
- Depressing the throttle pedal (manually, or automatically with cruise control engaged) signals the torque converter clutch to unlock when the load increases slightly. (A more drastic load increase would signal the Transmission to downshift to a lower gear.) The corresponding increase in engine RPM and output is enough to compensate for the reduction in speed. When the vehicle speed, engine RPM, and throttle position stabilize to the point that the TCC will engage and the engine RPM will reduce in correspondence with TCC engagement. Now, if the road conditions have not changed, power output is not enough to maintain vehicle speed. With the increased load caused by full engagement between engine and transmission, and the cycle (surging) repeats itself until the road conditions change.

Does that help?
If not:

QUESTIONS
Please define the symptoms.
What are the road conditions when the surge occurs? (A slight uphill grade?)
What is the frequency of the surge?
Does the engine power output have a noticeable surge?
Is there a speed change related to the surge?
Does the tachometer move up and down with little or no change in vehicle speed?
Are all instrument indication in the normal range?
What else has changed?

Good luck!

hot engine or cold, or both???????????????????
surging or hunting idle is complex but for sure the ECU has lost control of idle speed , there are 2 macro reasons, (vast causes)
1: ISC is stuck (in non SAE terms, the idle speed control valve ) is stuck.
2: engine is missing cause the ISC to GO NUTS trying to control
idle and can not.. the 50 reasons, , have list ask.
we do tests to find out if either or both the above are bad.
do you want tests, or guessing>???

you sure your engine isn't surging... you would see it at lower speeds... my motorcycle surges at a certain rpm due to fuel ratio's at the one speed ( running lean )... so what i am saying is, could it be that the engine surge only shows itself at a certain ground speed.

or is it because of a hydro system pressure relief valve ???

ENGINE SURGING COULD BE WEAK FUEL PUMP, STOPPED UP FUEL FILTER,BAD TORQUE CONVERTER SOLENOID OR TORQUE CONVERTER. OR FAULTY TPS.

Surging engines in lawn mowers are usually related to a lean fuel/air mixture. With today's environmental concerns, the carburetors on these engines are set with a very lean mixture (to reduce air pollution). Furthermore, they usually put limiter caps on the carburetors where you cannot easily adjust the mix to get the engine to run better.

If there are adjustment screws on the carburetor, try turning the high speed adjustment screw a bit counter-clockwise (if the limiter cap will allow it). This will enrich the fuel/air mix a bit and might help the engine run a bit better.

Its a loose connection on the speedo cable. its a b*tch to get to. I had the same problem on my truck, it would fluctuate in 5th gear on the highway. i spent the money and had a professional do it.

1980??? didnt have any sensors ,distributor cap points and carb ,zenith carb as i remember and bosch points and distributor

Sounds like a possible vaccume hose leak?

Try a simple test. It is ok to run the pump without water for a short time. Check idle speed without water in system to see if enginet surges. If it does not surge, then most likely the unloader/ pressure valve is causing the engine to surge when in the unloaded state. Life of unloader /pressure valve is shortened by letting system bypass for long periods of time. Enjoy