Hi and welcome,
Once you set pause_homing to True the second time, it goes out of your last while loop, and then ends the run function, and the thread. run is executed only once, when the thread is started.
If you want you thread keeping running forever, you need a while True, but then you need another condition to terminate your thread
def run(self):
while True:
if self.pause_homing:
# sleep
else:
# process variables
if self.stop:
break
It may be better to stop the thread when you are in pause, and to start it again when you are processing.