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I had the same problem a few weeks ago. I replaced the high speed blower relay, (by the evaporater housing, above the blower motor on my 86) and it didn't fix the problem. It turns out the wire on the starter solenoid was a little loose and dirty. This was the large lug on the solenoid...where the battery cable goes. There is a smaller wire coming off that same lug that goes directly to the high speed relay. Cleaning and tightening that connection fixed the problem. If yours works on lower speeds its probably not the blower motor. My guess would be the relay, switch or maybe what fixed mine...a bad connection.
Success story........
I located the hi speed relay but it was below the blower motor on mine. I had to remove the rear of the wheel well and side panel (shark gills) to get at it. I snapped the cover off and ran some 220 sandpaper across the contacts and it was good as new.