I am a Connecticut resident, get to SoCal a few times a year.
As is the case when I use it on the Canadian border, no problems.
Border people knew what it is. Pedestrians thought it was a cool
curiosity piece. I have used it myself into TJ at least 3 or 4 times.

You should not be checked upon entry into Mexico , only during
return to the US. I have never been stopped on the way in.

Note: When leaving Mexico at Tijuana, the Duty Free shop is about 100 yards from the entrance. The line often extends to 300 or 400 feet or more. If you are going to the Duty Free shop, go there by walking next to the line on the right side, don't wait on line until you get there. When you leave the shop get on line as soon as you get outside.