I guess that is a good plan at this point. New sender. It is possible you somehow sent voltage to sender and burned it out. It is also possible you sent wrong voltage or voltage to wrong gauge post and burnt it out also. It is possible you did nothing wrong and have bad parts due to age and etc.
Don't throw anything away.
In continuity mode, multimeters have an error display of 1 or OL, which means open loop, broken wire, not connected, no continuity. Sorry that I did not pick up on that error reading of "1" the first few times you said it. Seems like sender is bad. At first you are reading good becase the wiper on the sender rheostat has not reached the broken section. When it does, meter reads 1, the display for open/broken wire. Hopefully that is the explanation. BE SURE to test the new one on the bench. (just multimeter hooked up). Always touch your ohm meter leads together before test to get a small reading, showing that meter is good.
If bench test of new sender shows approx. 0-30, then test sender laying on the seat of the truck, hooked up to gauge and to a good ground. (preferably direct to battery neg post). BE SURE YOU HAVE THE CORRECT VOLTAGE AND KNOW WHICH POST IS HOT ON GAUGE. You may need more study and advice on that. When setup is ready turn the key on and operate float arm.
If gauge still reads wrong, unhook sender from gauge and ground. Retest sender, with multimeter, right away on the seat. If it still is good, it's the gauge OR the gauge ground. Then you take out gauge and take sender and gauge to bench and do the DADS50 test as seen in his video. Again be sure what voltage the gauge wants and which post is the hot post. (Once the correct hookup is determined, you will proceed with the test). This test will eliminate any bad wires you have in truck and will eliminate any grounding issues you may have in the truck. If the parts work together on the bench, all you have to do is install all new wire and fix all the grounding spots. Please report test results mentioned before going "haywire" on us.
The hookup of both parts on the bench is: Power source positive wire (battery charger or a battery with correct voltage needed) to hot post on gauge. Wire from sender post on gauge to sender center tap. Power source negative wire to sender flange AND to proper gauge ground metal. Post a picture or two of back of gauge here. Should be a round ground "slug" between posts. NOT SURE. DADS50 can verify where he attached ground on gauge for his video. I believe the posts on the gauge are isolated/insulated.
You can us the same multimeter, set on DC voltage, to measure output of power source to see if it has correct voltage for gauge. Be careful, be safe, double check setup before power on. Have good connections of test leads and wires.
We will get there and you will fix this problem and start answering questions about this issue for others.
P.S. A reading of 1 in the left side of display can also mean "out of range". Which means wrong scale or resistance unmeasurable. When you turn on your meter and select ohms, it should display 1 if leads are not touching. Touch leads and it should read 0.2 to 0.5, test lead resistance. If when testing a component/wire and you get "1" and you suspect you are on the wrong scale, change scales. If, each time you change scale, the "1" stays at hard left but decimal moves to different spots, you do actually have an open loop. It's not a range/scale issue. Some meters, in ohms mode. will have OL meaning overload. Which can still mean open. It can also mean unmeasurable range.
It is also possible to damage meter if power is on during continuity tests. At the least, it will NOT give an accurate reading.
