The one in mine has hardened and is broken up into several pieces. The parts list call it a locating damper which is also what the call the two round rubber disks that lock the front of the tank onto the frame. It's obvious what they do but the one in the back doesn't seem to have such an obvious purpose. I put my tank in place today and once the bolt at the back of the tank is tightened down the tank is solidly locked in place so not sure I even need the back damper as I can't figure out what good it would do. Having nothing else on hand to use I stuck a piece of foam rubber in it's place just because but don't know if that was even necessary or not. Anyone know what this piece is all about?
 

i think you want this puppy because when its positioned on the top bar the tank presses over it to create a slight interference that will dampen vibrations which could concievably cause seams to leak.   I have same bike and never tried without so i cannot say for sure.  If you need a new one i think you could get from KDI reproductions.  I secured mine to bar with a thin ziptie so it doesnt move around when taking tank on or off. 

good luck with the bike!

I was looking at the cable routing diagram in the back of the service manual tonight and I see that the main wireing harness passes through the damper so I'm guessing that it's purpose may be to keep the wires from chaffing against the inner tank walls. Just guessing on this but seems logical. I ran my harness between the foam I put in there so that should take of that. It also appears that the tach cable passes through the damper as well so I'll have to take a look at that tomorrow and see if that looks feasible.

The PO of my bike removed several rubber dampers and rode the bike. Result was cracked metal , where no dampers were ( chain guide, taillight bracket, rear fender...) The vibrations could kill the tank without that rubber underneath the tank, I guess 

 As far as I can tell no one sells that part anymore. If anyone knows of a supplier send me a link. In the meantime, the tank already has rubber at all three mounting points so that should absorb most of the vibrations and my foam padding might help a bit too, or not.  But either way, it'll have to do until I can find the real thing. Thanks

How about this?

Funnily enough, I've just bought a part from him - he's got some nice parts, but has (or at least had) got some of his listings mixed up between 1973 DT3 and 1974 DT250A! 

1974 Yamaha DT250 Enduro Gas Tank Rubber Damper Bumper DT dt 250 | eBay

This site has lots of rubber parts for these bikes too. 
this one should fit your bike. 
www.claussstudios.com/store/p658/Yamaha_...363-24183-00-00.html

Thanks Gr8uncleal, I just ordered it, looks like DT 250s and 360s took the same part in that year. I guess I couldn't find it because he has it listed for only a 250 and I was looking for one for a 360. Lesson learned. Thanks

Thanks Chuck,  that part looks like it would fit. Decent price for a new one too but his shipping costs more than doubles the price. Appreciate the site link though, will likely use it in the future.  Thanks.

One of the great things about Partzilla and CMSNL is that they both show which other models a part was fitted to, subject to a model's parts list being on their respective databases (most North American models are, but not many UK, Euro, Antipodean etc models are  ).