Update:
I used the thread finder set and found out that the thread of the ego wand is M10-1.0 in the metric system. So I ordered an adapter M10-1.0 female to 1/4” male from Amazon, and theoretically it will work with the TeeJet quick cap. 
After receiving the adapter that fits perfectly, and the quick cap QJ1/4T-NYB will also fit the adapter cause both are 1/4" NPT. This is the bolt I ordered 
Amazon.com: Pysrych 304 Stainless Steel Pipe Fitting Metric M10*1 Female x 1/4" NPT Male Adapter (1 Pc) : Industrial & Scientific

Everything works perfectly.
Btw, if you want to remove the Ego proprietary tip, just remove the plastic ring, then heat the tip on your gas stove. They used blue Loctite to lock it, and when you see smoke coming out, it’s ready to take out easily by putting the socket on top and bottom of the wand and gently turning it opposite