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About have to cut access if more is needed, then patch.
35 years ago I needed an antenna after I broke my stock 3 piece telescopic one. I robbed a antenna with base from a '73 or '74 Plymouth in a junk yard, it's the one with stainless steel mast. I made it straight with a bend. the cable and mount drop in through the hole. Still there. A 10mm open end will remove it in a few seconds. Sometimes I leave it off, plug the threads with a SS bolt.
The cowl area is a welded up air box that directs fresh air through the side vents at your feet. There's no direct access without surgery to make room for a power antenna. There are pictures of what it looks like in that area behind the fender and under the cowl box in this thread, here...https://www.ford-trucks.com/forums/1...ender-gap.html
Just to be clear, to get the part off in your picture, pop the snapped on chrome cover off with a small flat tip or pick. Remove the 4 short s/m screws and then have the antenna disconnected. Then remove the base and cable as one piece. The hole left maybe big enough to stick 1st half of your thumb in.
X2 to get in that area that is to the left of the glove box, and under the antenna hole in the cowl...well 1st there is a inner cab wall, AKA a kick panel, the inner part ends up being the pinch seam that the front of the cab/door seal is attached to. Not sure how big the power antenna base is, but you are probably going to have to cut a access point in the kick panel.
If you have carpet on the kick panel remove it, remove the glove box liner, if you have a/c that far side passenger side air duct is going to be over there also. Might be able to cut a access point in the kick panel and leave the a/c duct alone and work below it.
In the diagram below, do you see the small hole just aft/touching the side of the passenger side cowl? There is a rubber plug in that hole and that is the firewall that turns into the top part of the kick panel.
None a/c truck heater fresh air box only.
Pay no mind to the shifter, but look in the back ground and in the glove box. See the one round black plug?
And see the other round black plug closer to the back side of the dash?
Not sure about where the cowl "bucket" exactily falls out over there.
Didn't think about going through the vent opening, don't know what has to go in, but after seeing pics above .... the cowl bucket floor does extend below that pinch weld, and the kick vent hole is above the pinch weld a bit. just saying ...................