If its just J, then its probably related to when the battery was supplying power.
It's probably worth checking for circuit continuity, that will help show if there's a loose or poor connection without having to get under the dash.
When you're ready to start replacing components, the factory diagram shows the Fusable link was 16 gage. If you're going for original appearance, insulation was dark blue.
Crimp the fusible link to Packard 56 (or sometimes called Packard-Delphi 56) terminals for 16 gage wire. Use a good crimper with jaws for "open barrel" terminals. I finally broke down and bought a decent one which comes with a variaty of replacable jaws (Astro branded). Worked great on the females. Unfortunately the jaws are just a little too wide for the male terminals. :(
here's a close up of open barrel crimp jaws (borrowed from civilianjeep bb:
BASIC WIRING 101, Getting You Started! - JeepForum.com)
View attachment 1715099186
and a female terminal crimped
View attachment 1715099187
To remove the females, use a flattened cotter pin, tiny screw driver, or the tool they make for it to depress the tab while pushing it out. (The double prong version doesn't work well on the some of the mult-wire connectors like the bulkhead. The second prong gets in the way)
To remove the male terminals, you have to squeeze the open part while pushing it out.
View attachment 1715099188
The terminals can be often be had at the parts stores. If not, you can mail order from Waytek Wire, terminal supply Company, etc. Or you can sometimes get a few from someone here who has more than the need. I like the tin coated ones.
Before hooking up charge the battery.
Unless you find a smoking gun, have a helper when you do hook up. Be ready to disconnect the battery quick.
Do some voltage checks once its hooked up. Things like: should be battery voltage at the J and P terminals. Watch the ammeter too - should be no flow through ammeter.
If you want to test hot with a circuit breaker before trying a new fusible link, I'll see if I can find that MTSC.
Here it is, They suggest a 5 amp breaker (or a 4-way flasher unit). A test light on it would make it easy to see if power was flowing to a short.
1967 Chrysler Imperial Electrical Accessory Circuit From the Master Technicians Service Conference Session 236