Lol
You're short circuiting the earth there pal.
Attach the croco clip to the end of that black wire, and then do that again with the earth casing
Just editing my reply here George: there's 2x logical things we need for that horn to work.
Firstly with the horn off of the car like it is, we need to establish that it works, by that YouTube video, it looks like you're putting both probes to the metal casing, causing a short circuit as I said above.
Being a circuit, your principles for it to work, should be 12v positive (your red croco clip) to attach to that black wire (12v input) then your black croco clip, needs to be on the earthed metal casing. This should create a circuit making the horn sound. It shouldn't work backwards however, as that would suggest you've got a +ve chassis and not a standard -ve or earthed chassis (ridiculous as it sounds).
If that horn doesn't make a noise then, there's the problem. You could take it apart as Datsun were clever with be able to tune them slightly I believe?
The 2nd logical thing is that the wire that goes to the horn, from the horn pad. Is that wire working at the horn end? Put your light up probe between the wire and your earthed chassis. Have a helper press the horn pad, it should light up. If not, there's your problem.
Remember, you could have 2x issues here. Horn and horn pad.
I've been drinking and have too much free time this evening.. sorry for wall of text