I am self-employed & have claimed my vehicle under my business in previous years. Last year, I did Postmates deliveries on the side. Can I claim the vehicle for both?

Yes you can do that. It adds a bit of complication since you will need to allocate the miles and other expense to each of the businesses. Each business should have their own Schedule C. 

Thanks! I kept my mileage tracked separately, but if I'm not doing the standard deduction the gas, vehicle repair, and such were not tracked separately. It's not really feasible to calculate gas separately because a tank was used for both business lines and personal use. Would I enter the same amounts for these things in both places?

Also, I know that if I took standard deduction previously then I need to continue to do so; however, to the best of my recollection I did not. Is there a way I can tell whether I did by looking at my previous returns?

I still need help with the questions in my comment above!