I purchased some emulsion for cold light exposure, but I can no longer get the exposure times exactly right. If I expose the frame for 15/20 minutes, the lines printed on the gel aren’t visible. Perhaps the stronger the light is, the shorter the exposure time needs to be, is that right?

That's correct, the stronger the light, the shorter the exposure time.

So, if the lines aren't visible, the exposure time needs to be reduced.
I don't know what exposure system you're using, but we know for sure that, for the same exposure system, the ready-to-use emulsion for white light needs to be exposed for approximately half the time compared to a diazo emulsion.

I suggest trying an exposure time of 10 minutes, if the lines are still not visible, try 5 minutes.

If the exposure time then proves to be insufficient, you can always increase the number of minutes until you find the correct intermediate time.