I was wanting a sealed battery, so went to ebay and typed in motobatt for 1974 Dt 360. The one I ordered the ad stated it was for my bike. I did not look at size (my fault). When it arrived I saw that it would not fit my bike, so I sent a message to the seller asking what I should do? I never received a message from him, after my 3rd message I went through ebay and got a reply to send back. The seller goes by the name dbelectrical in Tennessee.
Looks like they do not make a sealed battery that will fit my bike.

This what I use in my 250A, www.ebay.com/p/1837198850 . There are several different brands. They last forever, it's been so long since I even looked at the one in my 250A I don't remember which brand I have. I do have it on its side with both terminals well insulated and the positive terminal at the top so it can't make contact with the metal compartment. The negative down and it doesn't matter if the insulation wears through and make contact. I think your 360A has the same battery compartment but measure just to make sure.

I use a large flash light battery for an earlier DT1. I've gone to this style on all of my small bikes.