Grab a new phone number from your phone provider (or use a one off non-published number you already have) and make all the techs call in on that number ONLY. (this also means you literally have to grab their phones and program it in yourself and remove your old "normal" number) This should become the new number for all staff to use calling the office at any time but not used or advertised anywhere else.
Make sure this number is not programmed to forward into ST software
Then it will never show up in your call screen for you to have to deal with.
You can set up a unique number from ST and put an "Tech Call" campaign on it...everything will end up in a nice report for you but you will still have to do all CSR "marking" which is a big time hog that I think you are trying to stay away from
Another thing we did (our phone system has this capability) is have that number have a unique ringtone from all other calls. This way when office staff is on the phone with customers etc and the phone starts going crazy ringing...you can tell if it is a tech and you dont have to put your customer on hold to deal with a tech at that very moment. You can just ignore and get back to them.
