Carousel projector problems often come down to lubrication having dried or become thick and gunky with age. Two places to look (with the case off and the unit lying upside down) are the tongue that moves the magazine and the solenoid between the main motor (not the fan motor) and the two cam wheels. The tongue should be able to move freely in both directions when operating and when changing between forward and reverse. The solenoid operates a toothed clutch but the assembly needs to be able to slide freely along the steel shaft so as to engage and release with a definite 'clunk' when an advance or reverse is required. You can check it by hand (with the power unplugged). If either of these mechanisms isn't moving freely, lighter fluid is very effective at dissolving claggy grease, followed by sparse re-lubrication - don't overdo it. The cam wheels benefit from a careful clean and grease such as Castrol LM (car wheel bearing) but the solenoid should not have anything that heavy. Note that the tongues operated by the cam wheels do so only when the machine is in its normal orientation and will appear to be doing nothing when it's upside down.
There's a site that may be useful at:
chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.tate.org.uk/documents/592/page_5_3_maintenance_slide_projector_0.pdf
and a parts site at:
https://van-eck.net/en/spare-part-finder/?cat=dia&merk=91&type=Carousel S which may be useful for information.
I used to work at a university where the Carousels got a real thrashing but very rarely did anything wear out if they were maintained properly. Resist any temptation to fiddle with the cam-operated electrical switches - they rarely give trouble.
Good luck!
Steve