The Simpson 260 is a good guess. If the criteria is same model, still looking the same, etc., I think we have to leave the first version (1939) out. It doesn't have the same cabinet type or look the same. The second version qualifies though. I'm not sure what year those started. 1949 sticks in my head for some reason. I have a second version with 1951 date codes in it. It is early enough to have no serial number, but I doubt it is the earliest.
Simpson 260 (260-1 to 260-8) 1939-2024 85 years
Simpson 260 (260-2 to 260-8) 1949(?)-2024 75(?) years
I'll advocate for 75 years until someone corrects me on when the "series 2" dropped (I could be a little off). That's going to be a tough record to beat.
EDIT: Make that 76 years, Radio's Master shows the old model in 1947 and the new one we are all familiar with in 1948. They are artists renditions so probably not definitive, but it's the best I've got.
The Chinese have the MF-500 VOM, still in production today, looking like it always did, somewhere in-between an AVOmeter and a Simpson 260. Like the 260 there have been a plethora of versions, and very different internal construction over the years. It is difficult to nail down much info about them, but I doubt they could reach back far enough to challenge the 260. It might be close. The AVOmeter could come close if you include all of them, but I'm not sure that's fair because the specs changed a lot (Ohms per Volt especially) if you include more than one model that happen to look alike. 1936-2008 gets you 72 years. Not quite enough. Another contender or close runner up, depending on how you look at it would be the Triplett 630, beating Simpson by a year (1948-2024) if my 1949 guess is correct for the Simpson "260-2". The problem is the variation in 630s has been wide, and the new ones don't look much like the earliest ones. If you allow that, then you would have to include the first version Simpson 260, and Simpson still wins.
The Fluke 8060a ran for at least 19 years (1982-2001). Can anyone beat that with another DMM?
Among other long running test gear is the Tektronix 545. Introduced in 1955, and TekWiki says that last 545B was in 1973 (18 years), but I believe examples as late as 1978 have been found and last I knew it wasn't clear when production really ended.
Then there is the HP 141T Spectrum Analyzer frame, from what 1971 to the mid or late 80s? Make that 1968 if you include the 141S with it's round screen and the same series of spectrum analyzer modules.
Someone already mentioned the HP 200CD 1952-1985. I think that might have really been 1986?
Weston had a long running small VOM, from the 30s to the 50s (maybe 60s?). The model number escapes me at the moment.
How long did they make Wiggys?