ground path goes from horn switch through cable reel through pass side under dash fuse box ( which at this point also splices off to multiplex ) to horn relay,, energizing the relay , relay closes , supplies power to blue/red wire that goes to the horns,,

You might want to do a temorary jump the wire at the pass side fuse box thus eliminating it, and a possible feed back from the multiplex unit ,, it is the lt green/blue wire, , it is the same color going in and out of the fuse box, you need to scrape it off a bit of insulation on both sides ( into and out of fuse box) and attach a temporary wire there ,,
see if that helps your issue and let us know. ..

be extra careful to get the correct wires and not to short them to a power wire or you will blow a fuse ..

I am also beginning to wonder if it is possible to loose ground supply through ign switch when key is inserted but i cannot see how ..

 

-will try the jump asDesert Honda suggestsin previous postthis weekend
-didn't check grounds at horn bracket yet as horn works with key out (does not work in any key position except off) since manual says left inner fender liner has to come off and if it works reliably in "keyoff " groundshould be OK
-I must say, car has over 100,000 miles on it since wife purchasedit new and the only unscheduled maint (besides tires/brakes) has been broken door handle tab (which I fixed myself with epoxy) and a very slow fluid leak from power steering rack which my mechanic says not to bother with (just top it off twice a year).

 

Worst case, you can run a new relay and wires from the switch to the horn.