I have a 1970 Plymouth B-body standard dash. With the voltage limiter removed, should there be continuity at the posts for the fuel gauge? With the wires disconnected, should there be continuity across the ammeter? Thank you.

Yes on the ammeter and the temp gauge & any gauge of that type must have continuity across it for it to function/register. on the temp gauge you hookup 2 AA batteries in series across it & if the gauge is good it'll read very close to halfway. I did my 65 Dart gauge but I dont have the note I took on the hookups/polarity cuz there are (3) terminals plus the polarity (I'd Google it)

With the instrument panel out of the car is there a way to test the fuel gauge and see if it is good. If there is continuity, does that mean it's good?

Yes its good, the variable is the resistance from the problematic sending unit in the tank. I'd start by grounding the blue wire L connector that is on the sending unit threaded stud & see if the gas gauge swings over to F (key on). if so you are OK from the L connector forward then the prob is the sender ain't grounded all the way up front to the batt neg post or the sender unit inside the tank is bad (common). If it dont swing over work forward for the open & find that wire behind the DR kick panel & ground it & if no gauge peg then work further toward the dash.

Keep in mind..
The guage may be shorted and would still read continuity....
The best way to test as mentioned previously is to series a couple of flashlite batteries and connect up..

Just my $0.02....

if you pull the dash out you might as well make some jumper wires and hook it up to a 12v battery. use the terminals on the dash that the wiring harness plugs into.
12v to the gauge feed, ground the dash through one of the bolts or something i think...then see if you get 12v to the voltage regulator and 5v out of the reg. you will see the circuit trace where it runs to you yr fuel gauge...that should carry yr 5v.

i hooked up some resistors and grounded the other side of the gauge with ~80ohms, 25ohms and 12ohms. i think that should be empty, half tank and full.

also you can use yr ohm meter to check the resistance on the wire that signals your fuel gauge, see if that reading correlates to what your gauge was reading...