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Both my 65 and 66 have the round cluster gauge in the dash insert. The 65 F100 has a silver painted insert with a black trim around the edge. It has an aftermarket Amp gauge on the left and an after market oil pressure gauge on the right. I'm wondering if there was an option for original gauges in these locations and what they might have been. I'm going to pull this cluster out to look at the wiring as my amp gauge bounces from zero to + 30. I just put in a new alternator, 55 amp, but am still using the original regulator. I have a lot of electrical gremlins to work out as it's been sitting for years. It starts and runs but no dash light, brake lights or passenger side tail light. Front driving lights work but come off when head lights are on. I'm going to check the head light switch connections and see if that helps.
The 66 F100 parts truck is missing the round cluster but has the insert which is painted white and has no gauge holes like the other one. Was that a different gauge option then my 65?
Although it's not the same instrument bezel as you are talking about, the factory amp gauge and factory oil pressure gauge are the same for both bezels and if you look hard at my picture you can see them as the outboard gauges. I would replace your voltage regulator if it's one of the old "points" units that was OE to your truck. I had no end of trouble with my old original unit and no problems since I went with a new "electronic" one. Good luck!