The speedometer and tach lights not working....

I believe yours is a cable driven unit.

So, detach cable at speedo head (knurled nut), unplug any electrics (lighting), or remove light bulb sockets, unbolt old unit and remove.

Reverse to install new unit.

https://www.manualslib.com/1/1989+750+yamaha+user+manual.html

with the handelbars turning on your rear brake light it could be you have some wires jammed and starting to cut through your other wires .take the headlight out of its bucket and check all the wiring around were it enters the bucket as for the low beam it could just could be the blown globe. cheers

Check the cables are not damaged if not lubricate them.

When the gauges quit, does the ABS light come on? Does the gas gauge and temp gauge quit too?

Could be bad brake light switch but turn signals involved so? Has to be bad ground.Light sockets corroded bad wiring thru fender mounting bolts in tail light assembly broke but corroded in place,not a good ground.Has to be simple cause bike runs.

better look at carb-there r 5 diff jets but its probly the mid range one-be careful here because rong ajust can hurt engine-u hav a clymer manual? library has many books on mc maintenance-sayonara

The drive gechanism in the wheel hub is damaged

The speedo head or cluster is the part that houses the speedometer and tach, etc. now it may be the speedo cable that comes from the transmission to the speedo head that has broken. If so replace the cable and your back in business. If it is the head you can get them from your local recycle yard.

There are 2 sensors on the engine that sent a signal to the computor and speedometer and tach. When one of these goes bad it can make the speedometer and tach go all over the place and also just stop working. This can also cause all types of engine running problems because the information being sent to the PCM will be incorrect all so. The units are easy to replace once you find them, it seems that they are located in different areas of the engine with each year the vehicle was put out.