K181 8hp with points and condenser, no spark

Before you connect the the electronic points eliminator please give the ignition switch a tub as per my previous post.
The modules are very sensitive to CURRENT ie AMPS and will fry if hooked up to a battery.
No idea is your 0.1 V will be a problem when running or if it is an accurate reading but at $ 50 a pop a good soak in WD 40 and some wiggling of the key is cheap insurance.
The module is based on the Atom unit invented down here in the early 60's but not universally adopted till the 90's when the patients ran out.
I can not see $ 50 value in it as the chip is around $ 1 .
Old Atoms are around $ 20 to $ 30 and the briggs module is around $ 20.

Good advice, I'll do that, thanks!

Now that I have the wiring issue straightened out I reassembled and reset the points, checked the timing and then tested with the pull start. I had to order a grommet for the fuel tank so I can't start it now but I checked it with an inline spark tester and I am getting a weak but very steady spark. The spark is weak but every few turns it will flash a bright hot spark. I have not replaced the spark plug, it looks okay but I'll see if that makes a difference. In the event that it is not the spark plug, is there anything else I should focus on as the cause of the weak spark? Is that more likely to be a condenser issue, a magneto issue or something else?

I appreciate the help so far. It appears that my main issue was the points not making contact. Once I cleaned and set the points I'm getting good spark. I did clean the magneto pickups and the magnets, they weren't bad but there was a little surface rust. I also cleaned the key switch contacts. I don't know if any of that helped but it sure hasn't hurt.

Turns out the wiring is back how I had it set originally so after all that back and forth the wiring ended up not being an issue. The help was necessary nonetheless because I had to make sure the wiring was right before I could go any further.

I'm anxious to try the new plug and to get the tank and starter on to see if I can get it running. Any other suggestions about the weak spark issue would be appreciated.

A bad condensor that is shorting out to ground can give a bad spark but more likely it is a speed thing.
The faster magnetos spin the better the spark.
Generally you test the strength with a 3 point spark tester.
A good coil will throw a 3/4" spark in air.
Cheap & nasty tester is a clear biro tube with a length of Copper core spark lead in both ends.
One end goes to the spark plug & the other goes to the spark plug lead, same as an inline spark tester .
You slide one wire along the tube to increase the gap, pull the starter then side it a bit further and pull the starter and keep going till you get no spark or the gap gets t 3/4".
In the old days when plugs were expensive we used this tool to force a fouled plug to work rather than the spark run down the side of the terminals.
Biro tube is a good insulator so you can move the wires without getting zapped.
In the 50's a similar device was a common bodge rather than fitting a hotter plug to burn off deposits.
Then in the 60's, 70's & 80's snake oil salesmen packaged the same thing into a little box called them Spark enhansers and sold thousands to gullible car owners who though you could get something for nothing.

Tried to start it with starter fluid since the fuel tank is not connected. It is still getting very weak spark and it will not start.

Question: Can I temporarily connect an external battery ignition coil and bypass the magneto just to confirm the problem is the magneto?

No.

I rechecked the point gap, it was 0.025. It is supposed to be 0.020. When they say that they mean it! I set it to 0.020. Got the fuel tank mounted. Spark looked good. Put it together and cranked it up and it ran like a champ!

:thumbsup::thumbsup::thumbsup:

Sounds like the condenser or magneto is not the best, but as it goes now , don't fix it.
Double check the spark plug grade to make sure you have not got a resistor plug.
The resistor plug is the same as widening the gap and if too big, the spark just does not have enough energy to jump.