Thoughout the 80's they made the multifunction LCDs that could function as cronographs and in 1988 they made a Marathon sports quartz cronograph with the "illusion" hands but no sub dials. In 89 and 90 they made some watches with 3 sub dials but they were not cronos as the sub dials were for day ,date and second time zone.
I am not familiar with the Timex models after about 1990 when everything seemed to go digital. I do have a 2000 Timex quartz crono that has a Miyota quartz movement,black dial and no rotating bezel. At the moment it is in need of a stem and crown. I will take a photo later.
Taro, on the 1958 Southampton the time kept going since the switch disengages the second hand from the seconds wheel thereby not stopping the train. The action is much like the mechanism that Pastor patented for pocket watches back in 1924.