I'm guessing the electrical components involved (relays/solenoids/etc...) for raising the bed are the same part numbers for lowering the bed. How I would approach this is start swapping like for like until I find the one component that the issue follows.
If you and Wolfman really want to get technical, you're referring to synchronous belts. But for the OP's sake, calling a notched v-belt 'cogged' is just fine as that's what many search results come back as.
I searched your original belt number and Messick's has a picture showing the manufacturer's part number, Mitsubishu REMF-6415.
Apparently Goodyear's 17425 cogged belt interchanges with REMF-6415.
https://www.finditparts.com/products/15356568/goodyear-belts-17425
Looks like M10x1.5 fits some Can-Am ATVs.
Could've gotten yourself a 4-pack for $4 with free shipping.
https://www.walmart.com/ip/4-Pack-ITP-Tapered-Chrome-Lug-Nut-10mm-x-1-50mm-Thread-Pitch/416345940
Took me a while, finally found it. The problem is that I'm not sure you can find a vendor for it.
Furukawa UW02F-B
https://ap-catalog.furukawa.co.jp/connector-web/productIntroduction/index.do?parts_name=UW02F-B
Took me a while, finally found it. The problem is that I'm not sure you can find a vendor for it.
Furukawa UW02F-B
https://ap-catalog.furukawa.co.jp/connector-web/productIntroduction/index.do?parts_name=UW02F-B
Same issue here- https://www.orangetractortalks.com/forums/threads/tractor-pto-sensor-plug.67902/
You're best off gluing the terminal into the housing.