In pic #1, Just below plug #2 and almost to the left edge of the water jacket cover we are looking at is the temp sensor with a black plastic shield/sleeve over the tan or tan lt.blue stripe wire coming right out the back of it. It closes at 195F with tolerances and shorts the wire to the block thus grounding the horn and making it blow. Above it, mounted vertically is the cover for the tstat and pop off valve; stat the smaller of the two bulges. Popoff kicks in at 2500 (serv. manual number) significantly increasing the flow through the block and essentially eliminating the effect of the tstat.
Agree with your comment about oil level and associated sensor wire. That's what I'd do on my personal engine if it happened to me rather than tearing out the tank and chasing the magnet and all that. If I were working on someone elses engine for hire, that would be the norm, but I'm not.
If you pulled the OT wire and it didn't change anything then you ought to be able to reconnect it to the control box wiring harness and you will have that protection after you eliminate the tan wire from the junction.
The Pee/tell tale/water stream comes from your exhaust manifold cover. If you refer to Pic #1 and look at the side of the water jacket cover mentioned earlier in my reply, just to the left of the OT sensor, there is a black hose running up the side of the cover and around to the left side of the engine; the big plate. That's the exhaust manifold water jacket cover and it gets water as long as the engine is turning and there is sufficient water above the top of the water pump for it to pump water to the powerhead. It has nothing to do with the block cooling so don't think that that will sub for an OT sensor. It won't other than if there is none, you know the engine is not getting water and will result in an OT.
Looks like you have a workable solution and it was cost effective.
Mark