If the the condenser is internal in coil which I more & more suspect,it probably serves the same function as a condenser in a normal points ign setup in that when points open a spike voltage up to 3 times supply voltage is generated for a fraction of a second as magnetic field in coil is collapsing,this spike voltage is induced into secondary winding of coil & boosts hv output,in addition spike also traveles back to source(points)the condenser across the points absorbs the spike voltage & reduces voltage in coil primary to as close to zero volts as possible before the next points cycle so you get max voltage buildup in primary of coil next time points close,in addition condenser prevents point burning/drawing an arc when points open,if condenser wasn't in circuit or if condenser open/shorted voltage would stay high in coil primary & have the effect of points staying open/closed all the time & no high voltage will be generated.
As far as solid state ign,I think the condenser in series with primary of coil is there to function as a buffer to protect scr in trigger so spike voltage from coil doesn't exceed piv voltage rating of scr,it may also function as a disconnect on load side of scr as usually when you use an scr in a DC circuit circuit when the scr turns on it will stay on an act as a latching relay till source voltage or load disconnected from scr so same can turn off,I found this out the hard way many yrs ago when I added foil defroster grid to rear window of my van,instead of buying a electro-mechanical relay I used a 20A solid state sw I had on hand,I killed battery in van 3 times in 2 days & couldn't figure out why,came to find out soild state sw was staying on/latched & powering defroster grid all the time after solid state sw turned on,even though sw on dash for sw turned off,only way to turn sw off was to disconnect load/supply voltage for a second or two.
As far as checking coil with a normal coil tester designed for 12v coils I don't know,it's something that would have to be tried,with condenser in series with coil primary if condenser open tester wouldn't work on coil,if condenser shorted it may give a false indication as to condition of coil or if coil working correctly,the only way I can think of to test solid state coil is to take a know good coil & see how/if it works with tester & use that as a standard when checking other coils.
Years ago I gave a thought to building a tester for trigger module/coil,however since that time either I no longer have engines with solid state ign or converted same to point ign as solid state systems went bad,just converting is an adventure in itself.
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