I have a Synder general furnance that is 22 yrs. old Model no.guf125ao16ain Serial No.0000211513-r03-0015
The furnance fan stays on at all times even though the thermostat is set at auto.I live in Michigan so right now it is a bit humid out.The fan runs even when the ac unit is not on.I have a digital thermostat.It is a Whit-Rodgers.The furnance and ac run fine when they are on.
If that furnace has a fan center unhook the wire going to g screw.
If the fan stops sounds like t-stat or a short to the g wire
If its still running it could be the contactor or could be the fan control.
That furnace might have the old fan control that turns on temp. rise, the points might be stuck closed or, some had a fan on button that would turn on the fan AT the furnace.
if you pop the stat off the subbase the fan should shut off if it stays on its the furnace/if it goes off the configurtion on te digital might not be configured for on/auto..as suggested emove the ZG wire at the furnace still on someting solid state board relay ..fan relay is welded tap it with a screwdriver handle