Old Carrier Furnace, 3-Wire Pilot Assembly, Electrode Sparks Continually While it Runs
I experience this exact same problem (sparking throughout the entire cycle) when the 646AX gas valve assembly failed and had to be replaced. No direct replacement was available but the stated equivalent replacement was the EF32CW.

I soon found out that the EF32CW doesn't actually have true separate PICK and HOLD coils -- it just ties the two connections together to energize a single PICK/HOLD coil. Unfortunately that means that the sparking that is supposed to happen only during the PICK phase now occurs throughout the entire HOLD phase.

My kludgy fix was to disconnect the fake PICK input and route the HOLD to the PICK. So the PICK signal only energizes the spark generator while the HOLD opens the PICK/HOLD valve and keeps it open. Works fine...