I doubt that relay click has anything to do with your blower problem.
Here's what I think is happening; there's a Blower Speed Control that regulates blower speed by restricting voltage to the blower motor. This is accomplished by running the power through a huge transistor mounted to the circuit board inside the blower speed controller.
Whoever made that board for Ford used a low melting point solder to hold the hot terminal to the board... we all know how hot these things can get... the solder melts and the transistor wont slow the blower anymore, hence; only high speed works.
The speed controller is mounted to the outside of the EATC unit, under the hood, behind the engine. It's hard to get at, it's directly behind the passenger side Valve Cover.
If you just re-solder the hot terminal to the board with some good solder, the problem should be fixed. Some folks just replace this controller too.
I don't have a photo.. hmmm.. let me see what's on the net.. BRB
Here's one picture from
www.p71interceptor.com :
(the soldered hot terminal is on he flip side)
( click to enlarge )