What are these electrical gizmos

[Javelinmania]

I am working on my truck and found a large numbers of wires connected to the starter rely on the post where the battery cable goes.  I was going to move them to the battery post cable.  Unfortunately, one of the wires broke coming out of this black gizmo.  Is this just a connector or does it do more like drop the voltage or as a fusible link.  Looking to see if I can just snip them off and put on modern connectors with a longer wire to easily connect to the battery.  I have not identified where they go to or what they are for - that is for another day.  The end with the eye hook looks like original wiring and on the other side is thicker red wires.  

[eaglescout526]

Those are indeed fusible links. 
 

How come you are moving them to the battery? Something wrong with having them on the starter relay? 

[Javelinmania]

When I look at the electrical manual, I do not see them on the starter relay and placing them on the battery would unclutter the area some.  Too many wires in a tight location.  They could easily go back to the relay.  Any thought on the amperage of the fusible link?  I am looking at the wires and I think several need to be replaced as the wires are not in the best of condition with missing insulation.  Some black tape could help to resolve the issue.

[AnotherOldJeepGuy]

I think I would take the one you are holding in your hand apart and see what is in there.  There could be an actual fuse in there and if so it should have it's rating shown on it.  It's possible you  fine out that these are just couplers that look like fusible links.  In either case the one you are holding isn't usable anyway, so nothing to loose by dissecting it!

[Eagle_SX4]

I don't think those are fusible links. AMC used those rubber injection pieces to cover wire splices near the starter relay. I recently did something similar to my Eagle. I added a fuse block to deal with all the wires at my starter relay. 

 

I got this one from Summit Racing. They have quit a few options for these from 4-10 fuses and ring or spade connectors. https://www.summitracing.com/search/brand/summit-racing/part-type/fuse-blocks

 

[GonzoTheGreat]

They are most definitely fusible links. I've always kind of wanted to identify the amp ratings and change them out for blade fuses, but at the same time, they've worked for 35 years, why mess with them? yours apparently decided it wants to be messed with. If there's someone on here with an electrical manual that can ID the amperage, you should be good to just get rid of it and use a fuse.

[Eagle_SX4]

I cut open all the ones on my Eagle and the were just crimped and soldered splices no fuses of any kind.

[AZJeff]

Fusible links were popular in some brands of domestic vehicles up into the early 1970’s.  Apparently AMC did it longer than others, probably due to budget constraints.

 

If I was redoing any power wiring in an older MJ/XJ, I would ditch the fusible links and put in a small fuse panel like show earlier in this thread.  It’s easier to diagnose issues and control power distribution with such an improvement,  and the cost would relatively low.

[Javelinmania]

I will be putting in fuse panel soon.  Here is what is inside.  The wires are different gauges.  The longer wire is a thicker gauge than the shorter one.

 

[Eagle_SX4]

That is exactly the same as the ones in my Eagle. Just a crimped butt connection that was soldered.

[llhat]

don't confuse fusible links with a fuse,  there's not a fuse "in" a fusible link.   the fusible link has a design where it fails at a certain load (amperage), this is done by carefully engineering the wire itself. 
replacement fusible link wire should be available at local NAPA or other FLAPS,  

 

but nothing entirely wrong with new regular wire and a fuse block.. choose your poison...    probably a good idea to consult the FSM (electrical) to see what each one controls,,  they are for different circuits.