Fuel gauge wiring question

I always adjust from the neutral position

Yes my IVR is a homemade deal and not a product by RTS. With a little basic electronics knowledge and soldering prowess you too can make your own

Yes the schematic shows 2 grounding points on my IVR schematic one ground point is on the mounting/heatsink tab, the other is one of the pins on the semiconductor chip. Always consult the pin out on the semiconductor chip bag for correct input, output, and ground pin location on the chip.

As a side note the NTE960 is designed to take up to 35V DC input and convert it to 5.5V DC output. Running 13V through it is nowhere near its maximum duty cycle. This chip should last for years and years.

Use a capacitor between 5 and 100uF and a voltage rating of 15V or more.

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I'm quite pleased to see "heatsink", "finned heatsink", and mention of compound noted on your drawing. Sure some portion of the heat would wick out into the mounting tang of the unit but we must understand that the heat is generated inside the chip. Thus the heat is concentrated in the part of that tang that is behind where we see NTE 960 shown on the chip in your drawing.
As the chip warms the output voltage will slowly rise.
I don't recognize the application shown in this link, Voltage regulator for gauge cluster – GoWesty but I can't imagine that chip living a long life without a lot of air circulation beneath the dash. I haven't found that in any vehicle. Brother and I put a lot of time in testing the different heatsink designs and different brands of regulator available at digikey. While I forget the brand name I/we settled on we did find what worked best/consistently. It would top out at 5.42 on the workbench with no load on the output.
I would order materials in quantities of 30 to 40. There was one time that Digikey took the liberty of substituting another brand regulator. Those things were all over the scale. Some would start at only 4.6 and climb to nearly 6 in same test conditions. Of course, I called digikey and pitched a biotch. They made it right after admitting what I had ordered was out of stock at the time.
So I started all this at about 48.5 yrs old. Today I'm closing in on 67. So much has changed during those What? 19 years. I did some reading around via a Google search yesterday and I must admit my brother understands much more of the data than I do. Today we would need to start over. I'll ad that a lot of what I found in search results was about 3.3 output regulators which I assume is related to LED applications.
In closing I have to suggest everyone just pony up for the RTE IVR for their gauges. Assume RTE is using quality components in their units and will stand behind whatever warranty they provide.
My IVR has never failed and I wont predict it will someday. If it does happen while I own the car, I will step up to the RTE unit. Enough said