When you jumpered the relay terminals 1--3, you BYPASSED the relay. This shows that the battery power to the relay connector is good, and that the wiring to the horn and that the horn itself is good
WAIT A DAMN MINUTE................You jumpered WHAT to the switch? (Post above?)
"The next step is to put the jumper between sockets 1 (to fuse) and 2 (to horn switch) and depress the horn button."
THAT IS NOT WHAT IT SAYS!!!!
Page 8-81 of the 1973 service manual
Horns Will Not Sound
Should the horns fail to sound, substitute a known-
good relay in the circuit and depress the horn switch.
Should the horns sound, the relay is defective and
must be replaced. If the horns do not sound, discon-
nect wire connector at horn and connect one lead of
test light to the connector and the other lead to a good
body ground. Depress the horn switch. Should the
light illuminate, the horn is faulty and should be ad-
justed or replaced.
If the light fails to illuminate, unplug the horn relay
and connect the test light to terminal "1" on the relay
terminal board and the other lead to a good body
ground. If the light fails to illuminate, inspect for
corroded battery terminals, dead battery or an open
circuit in the wire from the starter relay to terminal
"1" of the horn relay.
Should the light illuminate, touch a jumper wire
from relay board terminal "2" to a good body ground.
Sounding of horns will indicate a defective horn
switch or an open wire from relay board terminal "2"
to the horn switch.
CAUTION: Continuous sounding of horns will cause
relay to fail.
Horns Sound Continuously
Should the horns sound continuously, unplug the
horn relay from the terminal board inside the passen-
ger compartment. Plug in a known-good relay. If the
horns stop blowing, relay is defective and must be
replaced. Should the horns still sound, proceed as
follows: Connect one lead of test light to terminal "1"
on the relay plug-in board and the other lead to termi-
nal "2." Should the light illuminate, either the wire is
shorted to ground or the horn switch is defective.
Remove steering wheel trim and disconnect wire
from horn switch. Repeat the above test and if the
test light still illuminates, wire is shorted and should
be repaired. If the light does not illuminate, horn
switch is defective and must be replaced.
Don't take that flow chart too literally. What you are doing with the switch is you are grounding the coil of the relay, the other end of which has power. That should activate the relay. If the relay has an internal short or other problem, I can see how the horn wire to the switch might be doing that. I'm tellin you. From what you are describing, you have a bad relay. TAKE THE RELAY OUT OF THE CAR and pry the tabs off the top and take the thing apart.