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Check the ground wire. I started the blower motor and tested it by running a wire from the blower motor to a good ground. Most of the issues I've come acorss has been fixed by regrounding.
Ron
Not sure about the '68 but my '73 has the relay on the passenger side blower housing.
Pull the plug and test the leads for voltage with the blower switch on low or medium speed.
The reason I say low or medium is because the high speed setting has an inline fuse tucked under the drivers side inner fender (again, this is how it is setup on the '73 model, not sure about the '68) and if the fuse is blown you'll get nothing on your meter.
Oh yeah, to confuse things a little more my '73 has A/C