Nothin' worse than a finicky horn. They didn't use a horn relay in '49 so I'm going to assume you had to change the horn wiring a little. Originally one terminal of the horn was "hot" all the time, being fed right off the ammeter, the other horn terminal was wired to the button on the steering wheel and when pushed, that button would provide a ground.
My assumption is that when you wired in the relay, you're switching a hot lead to the horn and that the other terminal of the horn is grounded. So, seems to me the logical thing to do would be to isolate the problem either to the horn, the relay, or the button. If you short the hot lead to the lead going to the horn at the horn relay (you could use a screwdriver, a quarter, or whatever is handy) that horn should honk every time. If it doesn't, the problem is either the horn or the ground. If it does, test the relay with a short jumper wire to the other relay terminal (not the hot side, or the horn) momentarily grounded the horn should honk everytime. If all is well at this point the problem is either in the button or the wiring going up the column.