The picture is correct. Look at the letters stamped into the circuit board. The temperature, fuel and oil pressure gauges all have a terminal "A" and they are connected together. This is 5V coming from the original CVR. You could connect your new 5V supply to any of these terminals, since they are all connected together. The blue wire goes to terminal "A" of the temp gauge.
The fuel gauge only has two connections. It gets 5V from the CVR connection, and connects to ground through the fuel sending unit. The sending unit is a variable resistor connected to ground. The value of the variable resistor can range from 10 ohms (full) to 73 ohms (empty). By Ohm's law, this resistance limits current through the gauge, so the maximum current can only be roughly 12V/10ohms = 1.2 amps. Connecting the gauge from your 5V supply to ground provides excess current (limited only by the power supply and the gauge's internal resistance) and could damage the gauge.
Since you have a 5V supply, you could test the gauge on the bench with the resistances given in the TSM. 73 = empty, 23 = half, 10 = full. This means finding some resistors ... less than 15c of parts, but sourcing electronics parts seems to be difficult for you. If you can't find them anywhere, send me a PM and I'll put them in an envelope and send them to you. If it works on the bench, then you could test it in the car by unplugging the wire to the sender (pink wire under the Jeep) and connecting those resistances to ground on the chassis. Keep narrowing it down until you find the fault.
Actually Letank does not need that green wire, since the tab of the regulator is grounded and connects to the cluster chassis and ground there. When you mount the 7805 to the bare steel of the cluster chassis, you don't need the ground wire. However, your power supply won't work unless the ground is connected to the chassis somewhere.
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