Thanks everybody!
In the interest of brevity, I failed to mention that the electrical system of my 2000 F-150 was already FUBAR when I got it, presumably by a previous owner (or mechanic?), unless it's true that Satan still rules the lower world.... This makes troubleshooting exponentially more, uh, troublesome, especially as I'm working alone and hence have no one to depress the horn switch as I probe out the circuit. On reflection, it did occur to me that I can just jam a 2X4 between the driver's seat and the pad on the steering wheel to close the switch.
No need to do that, let's start fresh.
Find the horn relay, find it's pinout if it isn't obvious (e.g. two big terminals and two small ones, or printed on the case), briefly short out the relay contacts (B+ and HORN) with a chunk of wire, does the horn sound?
If the horn doesn't sound you go towards the horn/power side until you find the fault, check the horn's ground, check the B+ feed to the relay socket, inject 12V right at the horn and see if it even works, and to rule out trouble with the wire from relay to horn.
If the horn does sound, you go towards the control half of the circuit. Check relay coil continuity and relay function (connect 12V and ground with jumpers to the coil and see if it clicks and shows continuity on the contacts), then work back to the column and switch. I don't know how Ford usually wires stuff, but if I had to guess the relay circuit is probably a 12V feed on one side of the coil and the button just grounds the other side out locally to complete the circuit and close the relay.
That's pretty much the entire "traditional automotive horn circuit troubleshooting flowchart". On something this old and neglected you may find multiple faults, but again, it's a super simple circuit easily diagnosed with $10 in specialty tools (a test light and some jumper leads), and worst case, repaired with stuff you can rent from most parts stores.
Bad grounds to chassis and corroded connections in general are very common, always be looking, I've fixed stuff before by merely flooding grungy looking fuse and really sockets with WD40 and working the component in an out for a minute.
Another trick, if you have multiple identical relays in the box, you can just swap them between working and non working circuits to rule out the relay.
New parts are not to be trusted if you have not personally tested them.
If you have any working pro mechanic friends/family they'll probably provide connector pinouts, locations, and wiring diagrams if you ask, some local libraries also hold Alldata subscriptions you can use (same as the mechanic), Haynes/Chilton's will do worst case, you can probably easily find a scan for such a common truck.
The following is about all you'll need to figure this out quickly, note you can also connect the test light to 12V and use it as a ground tester. It also finds blown fuses as fast as you can probe the two probe points on top of each. I don't like using a DMM to check for power, 10 megaohms isn't enough load, I only really use one for ECM signals and references, ohming out connections, checking drop on cables, etc. You can't beat the test light for go/no go testing.
https://www.harborfreight.com/36-inch-low-voltage-test-leads-66712.htmlhttps://www.harborfreight.com/612v-circuit-tester-with-5-ft-lead-63603.html