According to the wiring diagram the stator timing/trigger pulse goes from the stator to the remote start module via a Blue/Yellow wire. The remote module routes this signal over to the CDI via a White/Black wire. If you unplug the remote you will need to jumper these two wires together to bypass the remote start module. The reason this signal goes through the remote module is so that the remote can kill the spark (and therefore kill the engine) by interrupting this signal path.
But I would still do the simple stuff first. Make sure the CDI is getting power (use your test light if you want). Make sure the CDI is getting a good ground (Black wire on the CDI to engine ground - use an ohmmeter to verify continuity).
I don't know what method you used to determine that the stator is good, but if you didn't use a meter then you're just guessing. Your stator has two completely independent systems inside. One is for charging the battery, and the other is for triggering the CDI to fire the spark plug. Just because one is working doesn't mean the other is working.
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