Your transmit and receive pairs need to be just that – pairs. Single wires would not cut it trying to carry 10 megabit data rates. Particularly with this pinout, since pins 1 and 4 in your jack should be paired together. The crosstalk after just a few feet of wire would wipe the signal out completely.
If you need to run ethernet on one twisted pair, you should use 10base2 (thin coax) equipment with baluns. These convert the unbalanced coax signal into a balanced signal usable on twisted pair. They are available in many of the wiring products type catalogs. I’ve seen them most recently from DataComm Warehouse for $19/each, which is high.
I’ve modified a number of IBM3270 type baluns, which are available for $4 or so to work with 10base2. They are probably not as good as the ones built specifically for ethernet, but I’ve used them through a few hundred feet of good quality (Catagory 5) cable. These contain (at least the cheapest ones, which is what you’d want) nothing more than a small 1:1 toroidal transformer. You need to rewire the leads to connect it as a current balun, like this.
This does not provide proper impedance matching of the ~100 ohm twisted pair to the 50 ohm coax, but testing seems to indicate this doesn’t matter much.
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