In my case, resetting only Privacy & Location
did the job (but only temporarily, see update below!).
Try only resetting that before resetting your whole network settings for nothing!
Almost immediately after reset, the "Trust this Computer" popup appeared and after trusting my device appeared in the Develop menu.
Update:
I kept having regular issues with this (having to reset it multiple times per day, restarting Safari and a combination of other things) until I found the real fix here:
https://mcmap.net/q/240772/-ipad-is-not-showing-in-develop-menu-on-osx-safari
@BearSnowstorm:
One more tip to try - after trying many of the above suggestions I
turned off "Sync with this iPhone over Wi-Fi" in iTunes.
Voila! Got my iPhone into the Develop menu!
(for context, this is in Mojave 10.14.6, iOS 13.1.3, Safari 13.0.3)
My comment on that answer describes the same thing but updated for Catalina:
I had recurring issues with this and the only way I could make it work (sometimes) was to reset Location & Privacy, close Safari, unplug my device, etc. It was always a temporary fix though and the issues would come back very quickly. This however seems to work more permanently! I confirm what @Florian said: the setting was off by default for me, turning it on then off (after letting the sync finish) worked. On Catalina, this setting is named "Show this iPhone when on Wi-Fi" under General when you select your iDevice in the Finder.
Reading that answer my instinct was that it could not possibly make a difference, but it does! I have had zero issues since I did this. Try it!