My cars radiator fan wont blow at all anymore whats wrong?

I have a 1992 cadillac eldorado, first i would
like to ask if the radiator fan is supposed to
run nonstop whenever the engine is running

on these cars cause mine has done that as
long as i've had this vehicle. The fan
stopped working some time ago and the
local service shop replaced the fanmotor
with a new one and it worked fine for awhile,
until now, i told the mechanic before he
replaced the fanmotor that the wiring that
connects into the fanmotor looks kinda
crappy and are those the cause of the fan
not working (apparently not) but even before
they replaced the fanmotor when the
fanstopped blowing it started blowing again
if i just pushed or lifted the wire that
connected into the fan, so that's why i
suspected a connection error or that the
wires needed to be replaced or something.
And after they replaced the fanmotor the fan
has worked only slightly better, its still like it

has a connection error or bad wires because
the fan stopoed working intermittently and
just bending or pushing the wire a little bit
started the fan immediately, BUT NOW TlHE
FAN STOPPED WORKING AGAIN and even
pushing or bending those wires wont start
the fan anymore so i think the wire has
broken inside completely now. Offcourse
there's only one way to find out. Or if the fan
really is not supposed to blow all the time
the engine is running that the fanmotor has
blown up or something.