I have to disagree with the idea that Timex watches were never meant to be serviced.
In fact Timex published servicing manuals (including lubrication requirements) for many, if not all of their calibres (see here for downloads:
http://timex.digidep.net/manuals/
They also supplied many service parts/spares including complete balance and hairspring assemblies, individual wheels, stems, pin pallets, main springs, etc; I know this because I have a number of NOS Timex spares and "service kits" in my stock, picked up from estate sales of watchmakers working in the 60's through to the 80's. So very much not designed to be thrown away.
What is true is that the standard Timex servicing procedures were kept simple, with as little disassembly as possible. It was usually necessary to remove the balance and hairspring assembly from the movement to be cleaned separately, but this was normally possible without separating the plates, and the rest of the movement went into the cleaner without dismantling it.
Lubrication was also kept simple. The mainsprings had a factory applied dry lubricant that was not affected by cleaning solutions so no need to worry about oiling it. Pivots generally required only one grade of oil throughout the watch, including the "V-Conic" balance pivots which are amazingly robust, and I believe the only other lubrication specified was a grease for things like the keyless works.
I have an enormous admiration for Timex movements because despite being incredibly cheaply made, they seem to be almost indestructible. The number of examples I have picked up for pennies, which have not been serviced in 50 years or more (since they left the factory), have been generally abused (dents and dings in the cases that testify to a whack that would have instantly destroyed any standard non-shock protected jewelled movement, and a fair few of the shock resistant ones too), and they still run, albeit a bit sluggishly before a service......
And then 15 minutes of taking apart, a good thorough cleaning cycle through the Elma, and back together with a drop of oil, and they're running like new. There are not many marvels of Swiss engineering at 10 or 100 times the price that can do that. And they keep quite acceptable time into the bargain. I think their only real weak spot was the rotor bearings on the automatics as these are often worn to rattling, but they do usually still work.
Next time you get a Timex, don't treat it like other watches. Just take off the hands and dial, and the balance, then clean the rest as a unit. Keep it really simple because that's the way they were designed to serviced.