Intel 8259A: mysterious T bit doesn't fit the pattern
The 8259A can work with 8080/85 processors, or 8088/86 processors. The mysterious T's only appear for the 8088/86 interface.

This means you have to go to the 8088/86 documentation for a clue as to what they mean. 

These latter processors have a 256 entry interrupt 'table' (looking good, 'T' for table?) that the programmer must load with interrupt vectors. I notice that for 8088/86 the PIC transfers only one byte, not two, which squares with it only being a 256 entry table (one byte addressing).

If all the T's start as zero (which is probably/possibly the default power-on state?), then that gives you access to the first 8 interrupt locations in the interrupt table without further effort. Writing a different T field allows you to switch the interrupt target quickly.