Q: electrical on 1997 Ford Thunderbird

Rookie cbe0621eac06868b3efe0d8d1d3611e23c60d3114864ea2ec19a68cfbd3eebab
flasher lights going all the time, running battery down. Pushing flasher button only increases rate of flash, but will NOT turn them off.
(2) Answers
In solving your problem, I am assuming that there are no aftermarket accessories wired into the vehicle, like alarms, license frames with sequential lights when brakes are applied or trailer hitches. Also that it has the proper bulbs installed, if these are all okay, then I think you have to check the multi-function switch (the combination wiper, high beam and turn signal control) next. This is the one component that connects all the flasher bulbs to the flasher unit. This would be what I would focus on first.
I had a similar problem. I sprayed a little WD40 on the button, turned it on and off a few times - fixed it. I think there must have been some dust or dirt causing a short in the switch.