Furnace blower switching on and off. Limit switch or circuit board?

It's the board.

Sounds like you're doing good for checking everything, does your draft motor have a little 3uf capacitor? You could check that. You could read the flame signal if your meter has milli amps DC.

But, If your limits, pressure switch, and roll-outs are all closed, and the board is making a clicking sound..... its the board.

Seen this exact thing on a AAON Rtu a couple months ago, but it wasn't getting as far as lighting. just the induced draft motor, board would start clicking, pressure switch closed, draft motor would cut off and on. And gas valve would never get 24v.

Replaced the C board, flame sensor, it needed some capacitors, and she's burning.

Check for loose connections at the relay for the motor or related wiring and also at the thermostat...green wire/terminal is for blower control at the t-stat and circuit board...loose or frayed connections could be causing intermittent power interruptions in the circuit. Might be a defective blower motor relay which is not closing the contacts properly....pitted contacts... or the coil inside the relay is getting weak and not fully closing the contacts, etc.....replacing the relay would be a cheap option to eliminate that as an issue. If wiring and relay are OK, then further testing would be needed. Furnace brand, model and serial number? try a websearch with your issues and model number/brand.

I would check the limit switch and the roll outs by pushng in the red button in the middle of the roll outs, I just had a goodman with the same trouble it was about 2-3 years old and I solved it by resetting the roll outs on the fan cage there were 2 one on each side of the fan

I had squirrels make nest in my old chimney so I had a problem . Just saying..people sometimes fail to check those things .

Did you test the relay ?