FWIW, historic/collectible tag enforcement was never a priority until the driver abuses it (speeding, reckless driving, dui, driving it for a daily commuter and passing the same Trooper everyday, etc.....) or the vehicle is involved in a serious/fatal crash. Then, the crash investigation will determine if it was driven illegally. It appears in Colorado you only have to sign an Affidavit swearing you won't abuse the statute, in my old state you had to keep a mileage log book and present it when asked. The violation was a traffic infraction summons.
Frankly, the biggest problem with historic/collectible tagged vehicles was crashes due mechanical failure (bad brakes, hydraulics, broken steering components, broken suspension, manual brakes failing due to speed, etc....) and/or operator error (the 90 year old Driver thought he could still handle the vehicle at speed into a corner like he was 19 and/or the 19 year old thought he could handle a 3 ton car with manual steering, manual brakes and no air bags like his honda.......oh, and DUI)
I've owned and driven this little 45 year old red head for over 25 years and have never been asked for the drivers log. FWIW and no guarantee your results won't be different. Be safe.