Maybe this is helpful?
https://visitrainier.com/cayuse-pass-123/#:~:text=For%20more%20information%2C%20check%20the,height%20limit%2013%E2%80%B2%201%E2%80%B3.
From the website, says 13.1 so you should be OK, not sure if you would have to drive down the middle which would be a concern. It does say, no commercial vehicles.
I would ask, why are you going that way? I have looked at state campgrounds in the area and depending on the size of your trailer, you might not be able to get a spot that can accommodate. That is the reason we found bumping lake. There are some nice areas to camp off Hwy 12 and some off 410, but didn't have a reason to take 123 to connect them. However, glad I now know about that tunnel. I will avoid that if pulling my 5th wheel. I'm sure it is marked at both ends of the highway.