Thanks for the info. It sounds like a dedicated hard wire to the battery is the safer bet. This question was actually for a buddy of mine with a full sized pickup. My Jeep grand Cherokee has. 115v 150w inverter built into the console. It's amazing that all modern vehicles don't have that as standard.
Yes, if you are willing to do that, that is the best solution. Don't forget to include a fuse in the wiring, sized to protect the wiring from the battery to the inverter. You choose the wiring and the fuse.
The e-bike battery is 835 W-h, so charging at 120W is going to take over 9 hours to charge from a fully discharged battery. The equation is 825 W-h/120W/80% efficiency = 8.6 hours. In reality a full charge takes somewhat longer than this, but the additional time only adds a small amount of capacity.
Charging at higher power levels can significantly reduce the charge time, but it's not proportional. Calculate the charge time to 80% of full charge. Charging from 80% to 100% of full charge typically takes 2-3 hours regardless of charger capability.
Some have suggested tapping off the alternator output. While I'm no expert, I'm pretty sure this is so that the charger can only operate when the vehicle is running. Charging with the vehicle not running could leave you without enough left to start the vehicle. In easy conditions, given the large battery typically found in full sized pickups, this might not be an issue if the battery is new and strong. But adding in battery age, size, and environmental conditions, you could easily run into problems.
Again, not an expert, but I think there's not a huge difference between tapping off the alternator or the battery
if you are careful to ensure you keep enough charge to start the vehicle. In general, tapping off the alternator output should be more efficient if you bypass the losses between the alternator and the battery.
In today's vehicles, you might not have access to the actual alternator output. If the rectifier and regulator are integrated, by the time you get out of the physical alternator package, that might be the same circuit as the battery itself. Maybe some auto experts can chime in here.