I've actually never had a problem with a cold start injector on Toyotas, other than a little dirty. I have had to replace several 'temp/time' switches.
They made some changes in them within the first couple years. All of them, trucks, too. They changed the resistance values to get better performance.
(me? 5 years at the dealer, many more elsewhere)
You can test the injector for resistance. per TSRM. 2-4 ohms
http://www.cygnusx1.net/supra/library/TSRM/fi/FI_077.html
The TSRM does not go into testing the switch, but you can check some resistance values thru the terminals to see if they are shorted or open.
Also, the switch is heat/cold controlled. If the temp outside is more than about 65* (maybe 55*) it won't allow the injector to come on, to prevent flooding. Also, even in a snow storm, after 12 seconds of cranking time, the switch will stop supplying current to the injector.
So...
On a cold vehicle (and you may have to pack some ice around the switch for 10 min. ahead of time), you can pull the injector and place the tip in a jar. Start the engine to see if gas is spraying.
No spray right away?? Stop cranking, and wait a few minutes for the switch to get cold again from the ice pack. Then hook your volt metter to the injector connector, then crank again to make sure current is flowing to injector. None? Stop.
Pull connector to switch and then test for current to it by cranking engine.
Have current?? then switch is likely bad.
I do it in this backwards order because the overall system gets tested right away. It is actually a very simply design, and seldom has problems.
The switch is a 'dealer only' part, and is a bit pricey $$$$.
Now....there are other areas to check for a hard start problem. Any codes come up when you scan it, or check it ???
TPS, AFM, coolant temp switch for the ECU. Fuel pressure drop, usually due to a leaking injector, or check valve at the fuel pump (in the tank, bummer).:icon_mad: