Interesting. Who was the idea guy deciding that the pickup needed to be set back so it hid completely under the ashtray pickup cover?? First time I've heard that and not sure that makes any sense. I had a '65 Jazz, which was stolen in 1976 along with all my touring gear. In the early 70's when I was touring I specifically left the Ashtray pickup cover in place because I though it looked cool, but removed the pickup cover over the neck pickup.
Here's a shot of me playing my 65 in 1972 with said ashtray in place and the pickup is well hidden. I did find a another picture from a front looking to back angle and you could "sort-of" see the edge of the mounts. My bass needs a good wipe down there but in my defense we typically played 9PM to 1AM, 5-nights a week 50-weeks a year. I did that for 3-years; made really good money; and had a great time.
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I finally replaced my '65 Jazz in 1985 with an '82 Jazz that has a white bound all-maple neck and the 70's era pickup spacing. As much as I loved my '65, if I got it back, my '82 Jazz would still probably be my #1. That combination of the 70's pickup spacing (4" center to center) gives my '82 a little brighter sound and a lot more sustain than '65 had. Regardless of whether someone made that choice as an aesthetic or not, in my experience it produces a superior sound. It also growls quite a bit more easily than my '65 did with its 3.6" center to center pickup spacing. Just dig into the strings over the bridge pickup and she'll growl all night long. Having played extensively with both pickup spacing types, I by far prefer the 70's era spacing although the 70's era necks are crap (way too fat).
Here's my '82 Jazz:
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When it was traded in at the music store where I was working part-time (went back to college), the pickup covers were still in their plastic bags and hadn't been opened. So they were never installed on this bass. Fellow handling the trade-in immediately took those covers out and put them up for sale in our accessories case. So I didn't get them when I bought that bass a month later. Since I do move my plucking hand around to fine-tune the sound I want for the song I'm playing, I've never been tempted to put an ashtray cover on it. I dig into the strings directly over the bridge pickup to make my bass growl when needed and I couldn't do that with the pickup cover in place.