Question on TT aero helmet
 

I don't do TT, own a TT bike or helmet so the question is strictly because of curiosity. Watching a TT event, all riders will periodically put their heads down, thereby having the end of their aero helmet sticking straight up thus reducing the aero effectiveness. So why don't they make aero helmet with hinges on the tail so that when the rider put the head down, the pointy end will rest on his/her neck/spine instead of sticking up the in air? Of course, this might just be another completely stupid question.

This has been noted by manufacturers and some now are making bob-tailed TT helmets that have slightly more drag than the long-tailed variety in optimal position, but less overall drag as the rider moves his head around as they do in real world racing. Kask was among the first and their bob-tailed TT helmets are often seen on Team Sky riders. Bell/Giro current TT helmets have short tails compared to the earlier offerings. Louis Garneau also makes a short tailed TT helmet, the Vorttice.

Hinged? Not sure, but probably not UCI kosher.

Does UCI also regulate helmet design?

UCI have extremely strict tests a helmet has to pass (atleast on the track, I rarely race road but race track every week so I know more about those regulations). The helmets can't be used unless they have a little 'UCI Approved' sticker (like on many bike frames).
Don't hold me against those regulations, I just know that a guy was running around my local track asking everybody if he could borrow a UCI approved helmet because his didn't have one.

On the hinged design; I thought I had seen a design resembling what you had seen, a segmented tail body that had hinges between them so the tail 'rested' on the riders back, arguably making the optimal aero position, in theory. Maybe the UCI rule them out, I couldn't see why but they have started to make some silly rules (i.e. no aero booties for velodromes anymore).

The UCI has one overriding rule which states they can rule on anything they want. And they have specific rules on many things, like no armless jerseys, for instance. Another is that riding apparel can have no extensions to make them more aero. One rule I'm aware of that helmets cannot be modified. For awhile, some riders would putting clear plastic covers over helmets to make them more aero. This was ruled impermissible, so manufacturers started making helmets with the plastic covers permanently glued in place.

A hinged helmet had occured to me too .... or a weighted tail, and a pivot point inside the helmet between the strap & helmet mount, so that when you point your head down, the helmet stays on the original position.

Not a concern for us tri guys.

Can said tri-guys modify their own helmets?

Nope. But if a hinged helmet passed CPSC testing we'd be clear, no matter what the UCI thought of it.