2007 Cheyenne, made in Mexico, Charge Voltage is variable 12.6 to

I seem to recall that the high voltage battery has a module that identifies it to the car. If that is the case, you need to go to the dealership or call a mobile auto electrician with a pro grade scan tool computer to program in the details of VIN number and mileage.

There are some videos here. I haven't watched them but I hope they are useful.

https://www.google.com/search?q=2007+toyota+prius+high+voltage+battery+replacement

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There are a lot of possibilities. Bad starter relay, Bad ignition switch, bad starter solenoid, bad starter, anti theft engaged. First try hitting the starter while someone has the key in the start position.

Check the clutch start switch above the clutch pedal , look up under dash . Yellow wire going in, purple coming out ! Yellow should have battery voltage with key in start position. The purple should have battery voltage with the key in the start position with the clutch pedal pressed down .

Check the idle rpm (efi around 900 rpm ) carby around 750-800rpm. Very few alternators charge under 750 rpm as it requires 14 volts to charge the battery and at low revs the alternator will be producing around 11.5-12 volts. Check tension and condition of drive belt.

If you have a voltage tester check the voltage of the battery after you charge it. it should be 12 volts with the car off. then start the car it should read about 14 to 14.5 volts if the alternator is working. If the voltage stays at 12 its not charging and if it only jumps up a little its not charging enough to charge the battery

It is almost definitely a bad alternator, but could also be a limited number of other things. A bad battery terminal could cause this problem as well or other loose or corroded connections. As for your 12 volt reading on the alternator, I should explain a little about electricity. If electricity travelled down a highway, the number of lanes would be the voltage and the speed limit would be the amperage and the wattage would be lanes multiplied by the speed limit. 12 lanes travelling at 2 miles per hour aren't getting anywhere fast. Also, a car battery's charge voltage slightly above its' output voltage, so it should be roughly 13.4 volts up to about 15 volts.

Try to rev the engine while at neutral if you get the same vibration to pinpoint if its from the engine or the drive shafts. If the issue occurs at a certain rev it may likely be the variable valve unit. Check if possible if you can get errors from the computer.

most chargers have a few different settings you want to put it ona slow charge for about 4-6 hrs bye slow charge I mean it should have a 2amp or a3amp trickle charge unless you are attempting to start the car immeditly the you will you the setting labled starting

Perfectly normal.
Starting with the 2005 model year, light duty full size pickups and utilities are equipped with a new Regulated Voltage Control (RVC) system. This system reduces the targeted output of the generator to 12.6-13.1 volts when in "Fuel Economy Mode" to improve fuel economy. The generator may exit "Fuel Economy Mode" if additional voltage is required. This will cause the voltmeter to fluctuate between 12 and 14 volts as opposed to non-regulated systems that usually maintain a more consistent reading of 14 volts. This fluctuation with the RVC system is normal system operation and NO repairs should be attempted.