(1) Make sure no damned anything on your violet wire to sending unit under hood, sometimes people put carb return springs on it which instantly grounds it out. Pull the little boot off and crimp it with pliers so tight on sending unit also.

(2) Make sure your engine ground wire is intact and tight, this is on passenger side behind alt to block, to crossmember. If this is loose, or copper green or not there, you will have all sorts of electrical shit problems, the temp least of troubles. Get a $5 universal one at parts house.

(3) Pull your fuses and replace, whether good or not simply replace them. The little ass fuse controls both fuel and temp, and I might recommend putting some silicone grease on all fuses like I do with my AMCs here, as same clear grease used for spark plugs, but creates current and if you live in area with high humidity, then no grease causes them to lose continuity and contact. While under there, loosen and then retighten both 5/16th bolts holding your fusebox to frame also.

(4) Pull gauges from dash out and make sure the nuts holding the gauge to circuit board are tight, I would probably loosen them up, then retighten them. These come loose with vibrations and I wrote a few years ago my 68 Ambassador 4dr gas gauge never worked, then I was driving down I-10 after filling it up and since I had radio out there was big hole space there and I reached behind to gauges while driving 70mph and was surprised to feel the gauge nuts loose, tightened them by hand and gas gauge shot up to correct level and never a issue again. 

Pull your gauge cluster last it nothing else works. The best thing about this is it is easy to do, you only disconnect your speedometer cable, and can leave the wiring plug(s) intact. And while intact you can check your temperature regulator on back, and/or also hand tighten the nuts holding your gauge to circuit board while car is actually running so will see if any reading. 

(1) Pull your fuses and replace, whether good or not simply replace them. The little ass fuse controls both fuel and temp, and I might recommend putting some silicone grease on all fuses like I do with my AMCs here, as same clear grease used for spark plugs, but creates current and if you live in area with high humidity, then no grease causes them to lose continuity and contact. While under there, loosen and then retighten both 5/16th bolts holding your fusebox to frame also.

(2) Make sure your engine ground wire is intact and tight, this is on passenger side behind alt to block, to crossmember. If this is loose, or copper green or not there, you will have all sorts of electrical shit problems, the temp least of troubles. Get a $5 universal one at parts house.

(3) Crawl under vehicle and with flashlight, (don't be a Aggie & use lighter) but crawl under back and check the wires to fuel sending unit at gas tank. There should usually be a yellow and black. I recommend pulling off the black wire from frame, usually held on with eyelet and 5/16 bolt, but pull it off, scrape it well with razor blade so nice and shiny both sides. Make sure to put drop of silicone grease in hole before you put bolt back into it in frame. Be sure to check other end of this wire as many times they deteriorate where it goes to actual sending unit. If this is case, you will need to replace whole sending unit, or drain tank, pull it down, and take it off and sauder it away from tank.  

(4) While nosying around gas tank, pull off yellow boot at sending unit, check it well, you might have to crimp it and put back on, same thing, small drop of silicone grease in it, but it has to be on there tight, no looseness. Check wire to make sure it is not cut from road debris, can't tell you how many times I have ran over something thru years (and I have driven nothing BUT the fine cars of American Motors since 1976) but ran over something could be limb for instance, and it compromised this wire under car. Something else you wish to check is in trunk, follow the yellow wire thru plug. Many times in a AMC's lifetime something, could be spacesaver spare, groceries, jack, something slid across the trunk while owner was turning and it hits this unsheathed yellow 'hot' wire, and will cut it at the grommet where it goes thru trunk!

So while wire looks good from inside trunk, closer inspection might reveal broken sheath, which copper wires now touching metal, therefore leading to false inaccurate reading if any at all....or your gas gauge will shoot up past full! So look carefully around here, if you have to pull plug and inspect wire on trunk floor pan do it.