It's a low speed 120mm fan zip tied to an Accelero S1 (GPU cooler). It was connected to the Cha-2 3 pin connector. Like you, I had odd readings on the RPMs from that connection but I didn't try another.
I think we're on to something. Two boards with odd readings seems to suggest that there's an issue, at least on that fan plug.
It isn't a problem with the start voltage, since both fans that I tried started fine when the computer booted, and they also both started fine when I changed anything in the fan profile. I also just remembered that the fan RPM readings were in the 1200 range even when the fan was stopped entirely. It seems like the board is trying to slow the fan down, but its getting incorrect RPM readings. This leads the board to repeatedly drop the fan voltage (all the way down to zero).
This had always been the problem with mid-range boards. That is, there were either two few fan plugs, or control was inadequate. I may have had my mind on something else when I stumbled onto this problem, so I didn't spend enough time with it.
In my rig, a Noctua-NH-D14 is installed with both the accompanying Noctua fans, each plugged to CPU-Fan and Opt-CPU-Fan respectively -- a total of 0.20A @12V. CHA-fan 1 has an NMB-MAT Panaflo 120mmx38mm -- the exhaust fan -- at about 0.46A @ 12V. Previously, a 140mm x25mm fan -- something in excess of 0.25A -- was [providing intake at 1,500rpm, but even with that the tach readings are erratic as it was connected to CHA-Fan 2. I hadn't paid much attention to this until I wanted to thermally control a 0.70A NZXT 200 x 30mm intake fan to match thermal control of the Panaflo, and chose to hook it up to the CHA-FAN 2 plug. It wouldn't start.
With previous ASUS boards I'd had, there was a fan spec for the motherboard plugs that gave the total allowable amperage draw, and while the spec stated a maximum amps per fan (an average), any distribution might work if the total was in spec. But even this left something to be desired, because only certain plugs fell under Q-Fan control and the others ran at a % of top fan speed or amperage that you would set in the BIOS.
And that description fit only a top-end motherboard I bought. Other, mid-range boards allowed for thermal control of the CPU-fan only.
nVIDIA promoted something called ESA which worked with nVidia motherboards, and you could buy a Silverstone Commander controller with USB link to the computer. It came with sensors, and you could either set any of four or five fans at a fixed percentage of top speed on any one of them, or link them to a profile of speed and temperature. One accessed the controller setup through the nVidia software. It was as good as I ever remember. But these boards we have use Intel chipsets.
I might venture a guess that the total amperage allowable on the P8Z68 fan ports is insufficient. If that is the case, we're lucky to have thermal control of the CPU fan and the CHA-FAN 1, but I could wish for more.
I'm window-shopping fan-controllers which are software-configured and totally automatic. The ones you would want -- using their own microprocessor and temperature sensors -- are pricey.
I don't like manual controllers; don't need a glitzy front-panel with bar-graphs, knobs and buttons. And this is a P-I-T-A because it costs more and adds additional equipment and complexity. I either spend the money and add the extra circuitry and software, or settle for running at least two case fans directly from the PSU. I may do the latter if I can just deaden the white-noise from turbulence on the NZXT fan(s). On the upside, those things are rated at 166 CFM for airflow on each unit.