In the 1970s, the issue was most likely a four inch Model 10. I came in in 1991, and the old guys then had plain-jane Model 10s. These were replaced in the 80s with the now-iconic three inch Model 13s.
Most agents of that era carried something from the extensive personally owned weapons (POW) list. In 1991, any steel framed Smith and Wesson .38 Special or .357 Magnum with a 2 to 4 inch barrel was approved. The K-frames were popular, with the 2 1/12 inch Model 19 and 66 being the most popular. I saw Model 15s, too, and the L frames had a loyal following. By then, almost all of the steel framed 9mms and .45s were authorized, too.
I was a Smith man even then, but I couldn't find a 4516 anywhere. My Dad had an FFL at the time, and he ordered me a Sig P220. (All Sig 9mms and .45s were on the list, too).
Almost everyone had a J-frame, too, known in my part of the Bureau as a "five-shot".
A few of the real dinosaurs in the office had Colts - one guy had a Trooper and one had a Python. These were grandfathered in at the time.
I became a Firearms Instructor after about five years, and helped with the transition from the revolvers to semi-autos amongst the guys who were still carrying revolvers.
Once everyone was qualified on a semi-auto, the purging of revolvers began. In 2001 the edict came out that no revolvers were authorized for carry at all.
Until the first Clinton administration, retiring agents were allowed to purchase their Model 10s for a nominal price ($120, I think) under a special provision authorized by Congress. That provision was yanked, and the wailing that resulted was long, loud, and fruitless. Guys that had carried their trusty Model 10 for twenty years under the impression they would be able to take it into retirement suddenly had to turn it in to the gun vault for eventual destruction.
Once, a few years ago, I asked for some Simunitions guns for a hostage negotiation exercise. Quantico sent me a pelican case full of four inch Model 10s, complete with diamond mangas, fitted with Simunition cylinders and painted completely orange. That's where some of them went, at least.
I also saw some desk sets made up as gifts for visiting dignitaries. They had the vertical foregrips from our old Thompsons mounted on them, with a Model 10 or 13 cylinder expoxied on for a pencil holder!
As Texas Star noted, my old Sig is grandfathered in. Good thing I went with it back then, because NO Smiths made the cut for grandfathering.
Added:
I just read the OP's other post about the gun in question being a Model 60. I would be very very surprised if that was an issued gun, and before paying any long green for it I would give Mr. Jinks a call with the serial number for verification. As I said above, that is almost certainly a gun he either bought from a retailer and had added to his POW list, or bought from another agent, possibly under the impression it was an issued gun. Never say never, but Model 60s weren't standard issue to agents. There is a tiny chance it was issued as an undercover gun or for some other special purpose and he retained it somehow, but I doubt it. Its been so long he's probably not sure, either.