I get the impression that you have a mix of 1 or more single member LLCs, and I already know that you have "at least" one multi-member LLC. The single member LLCs get reported on SCH C as a part of the personal 1040 tax return of the legal owner of the business. Whereas the multi-member LLC (you and brother) gets reported on the physically separate 1065 Multi-member LLC/Partnership tax return.
Claiming a vhicle in multiple businesses of the same structure is complicated enough. Using it among different business types can be an absolute ever lasting nightmare from which you will never awaken. One teeny tiny mistake with just one business, can have a ripple effect (depending on the mistake) across all businesses making taxes pure hell.
Since the vehicle will be purchased with one of the businesses as the titled owner of the vehicle, and will be 100% business use (i.e.; not driven one single inch for personal use by anyone) then I would suggest the business that owns the vehicle, rent it out to the other businesses at something like a fixed rate per day, or fixed rate per mile. Then claim the vehicle as a business asset.
If feasible and reasonable, if the business that owns is the business that will drive it the least (or not at all) then it can be listed as a business asset that gets depreciated over 5 years. The rent paid to the business would be business income. The taxability of that income would be offset by the costs associated with maintaining the vehicle, which could include the cost of gas if you include that in the rental price.
For the business that owns the vehicle, it's expenses for use would be the actual costs to that owning business. I'm not sure,but I'm pretty confident that with absolutely no personal use, mileage logs would not be required. (But I would still do so anyway)
For the businesses leasing the vehicle, they won't need to keep mileage logs, since they would be paying a bonafide business rental expense for the vehicle.
