Not sure of the law, but does your employer allow you to carry a gun when you are working?
And would you be keeping it on your person while climbing poles, or keeping it in your truck while you're away from it? Either option sounds like a risk. Don't ever think anything in a vehicle is actually safe or contained - it isn't.
I would suggest that you read this article, because there are likely a lot of other factors involved, including proximity to hazardous materials, and being on land that may be restricted - such as a school. Obviously, with the itinerant nature of your job, you may very well find there are places you shouldn't carry it, and your employer could very easily decline to take the risk. You could be charged with firearms violations by not asking directly, so don't take a flier on this. Get it in writing, if they give you permission.
https://www.littler.com/guns-vehicles-company-parking-lots-now-allowed-in-texas
This is in fact on a slightly different subject, but goes through a lot of points that will be relevant to your case.