What does II mean on the small oscilling heater

If it is new, contact your seller for return or replacement under warranty
Manual
http://comfortzone-us.com/temp/CZ499R_manual.pdf

I had the same problem. There is no switch to stop oscillation in heater mode. But, you can stop it for all modes with some DIY.
Grab a phillips head screwdriver, and make sure the heater is unplugged.
Remove the 5 screws on the bottom base.
Once the bottom panel is off, remove the 2 screws in the grooved sections.
The base will now come off.
You will now see a cog - Which is what oscillates the base. It is covered in green lubricant. Undo the screw on top of the cog and take cog will come out.
Reverse steps to close everything back up.
Doing this removes oscillation permanently. Put the cog back in to restore capability.

S Adams, return for refund or replacement, sound like plastic gear inside could be damaged or loose. Check the attached links,instruction and guides, Good luck
"I hope this helped you out, if so let me know by pressing the helpful button. Check out some of my other posts if you need more tips and info."
https://www.dyson.co.uk/support/am09/am09-white-nickel/my-machine-is-not-working/my-machine-is-not-oscillating
https://www.dyson.com/support/am0112/am01-desk-fan-12-silver-iron/diagnosis-root-menu/my-machine-is-not-oscillating-am01
Dyson AM 02 Fan not working oscillating feature is broken
http://www.dysoncanada.ca/en-CA/support.aspx

beware of the materials that are used are usually very soft witch used by Fein in his budget machine class.
puler
Only a dutch version but the same parts positions.
MSxe 636 II 50Hz 230V

thermal fuse is usually the first to go check it for continuety

Electricity is not suitable for use by you....
Check power point with another appliance. Check heater switch, high temp, etc....

An oscillator? :vibration, motion like a pendulum, pulsation, fluctuation, rotation...yeah, I can imagine Nissan calling a door that swings back and forth to direct air, an oscillator. Hope someone is not pulling your leg, though, or we've both been suckered ! Don't know what to tell you, except to find your nearest oscillator outlet supplier. In the meantime, check the controls to the various doors on the heater case. Are they vacuum controlled, cable controls, or electrical motor controlled? Usually all of one type. You may be able to see the offending part, a disconnected hose or cable, or the stem of an inner door that has broken or not moving the door. The oscillator might be hidden deep in the bowels there-be careful. Good luck, norman.

if no heater on crt tube the tendency was no display, that means the oscillation is not working and therefore fly back transformer will not work. now how are you going to locate the problem first you need to check the regulator if good then the horizontal out put transistor if it is not shorted. if one of this major part is defective circuit will not work. vertical section will just only wait to the horizontal output to oscillate. and every section will work after horizontal oscillate. good luck hope it will help you.

Per your owner's manual:

AGS

(automatic gas shut-down)

1. Oscillating pump pressure.

1. Clean filter or identify and repair cause of pump oscillation.

2. Low gas supply pressure.

2. Identify and repair incorrect supply pipe size or pipe line blockage.

Refer to qualified service personnel.

3. No flame at burners.

3. No flame at burners. 3. Identify and correct loose wiring connections, or problems with igniter, flame sensor, gas valve, or ignition control.

Refer to qualified service personnel.

For more info the manual is here:
http://www.jandy-downloads.com/pdfs/LXandLT_H02140B.pdf

John