The shifter location should be the least of your worries.  Its going to be in the same spot as the T5.  The 3650 was a direct replacement for the T5 in Fox era cars.  It was the first Tremec to market, and continued in production alongside the TKO for a brief period before being phased out.  They could be converted to TKO spec, but that conversion is now probably cost prohibitive if the parts are even still available.  It was a pretty strong box, a buddy of mine has one in an SN95 Cobra behind a Kenne Bell blown DSS Bullet making 550+HP and its been in there close to 20 years without issue.

That said, all the 3650s are 20 years old now or older, and they weren't driven gently.  Guys swapped them in when they got tired of breaking T5s.

There are a couple issues I see with this trans in an early car.  First, its considerably larger than a T5 width wise.  In a Fox car this isn't an issue, they have a big tunnel.  A '65 doesn't.  I think it will likely hit somewhere knowing how close my T5 comes in a couple spots.

Second, if it doesn't come with the bellhousing get ready to drop another $280 for that.  They are not a factory part.  The Tremec used a different mounting pattern than the T5 due to its larger case.

Third, I've never been a fan of the way Tremecs shift.  They are super notchy.  It can be corrected with Hanlon Motorsports carbon lined synchros, but that requires complete disassembly, and while its apart might as well rebuild it. 

My $0.02, if you need the extra strength it might be worth it, if you don't mind modifying your trans tunnel.  If a T5 would work fine for your application its a cheaper swap that I know for a fact will fit, and the 3560 is just the wrong part that happens to be available.