What's the daily life like for a 35L or 35M?

If you spend 10% of your time firing rounds, you're doing a lot better than a lot of grunts.

35L requires gaining and maintaining a Top Secret/SCI security clearance, which requires a comprehensive background check and is only granted to those aged 21 and over. It also requires completing the Counterintelligence Agent Course (CISAC), a 19-week training course that involves advanced training in areas like counterintelligence investigations, operations, and analysis.
A 35M Human Intelligence Collector AIT is approximately 20 weeks, but the total training time can be much longer, often between 9–15 months or more, depending on language training requirements. The full timeline includes initial Basic Combat Training, followed by the AIT at Fort Huachuca, and then a foreign language school component at the Defense Language Institute (DLI) if required.
Both MOS's are a far cry from being a Cannon Cocker!

It’s a military law enforcement job, with badge, creeds, firearm and apprehension authority. It’s rarely playing cop though, mostly analysis and investigative. If you do a career or last 10 or more years, you generally qualify for LEOSA retired federal law enforcement credentials. I worked in the field as an MP augmentee as I had done so in the USMC and I was a state credentialed criminal investigator. It was interesting and required work and brains, but very little excitement.