Looking at the historical use of T-tails, it seems that the primary advantage was to make room for tail-mounted engines. Which doesn't say much about the tail itself, other than - it had to be someplace the engines weren't.
(And even then, there were the L-1011 and DC/MD-10/11)
A lesser advantage - to make c. 1970-designed bug-smashers look "F-104 supersonic cool" even sitting still on the ramp. Generally, the lower the power, the more prominent the T-tail.
Kind of the aviation equivalent of 1950s car tailfins.
The F-104 itself is worth some research - it was given a T-tail to counteract the likelihood of inertia coupling (wild gyrations on all three axes with control input) due to the long thin fuselage and stubby wings. In the event, it may have created as many problems as the one(s) it solved.