"What if there is no provision for the use of a personal truck."

Is that how I worded it? Let me review a few things to know and/or research.

I can lease my truck to the LLC. That means I get a 1099-Misc Box 1 for the Lease income to me and the LLC gets to list their expense, and I don't use the truck for Personal any longer.

https://smallbusiness.chron.com/need-issue-1099-leased-business-equipment-64287.html

Or, it's still my personal truck and I am allowed (and it is safe, insured, etc) to use it for LLC work. Not just for Vehicle, but in general, the partnership documents (LLC) need specifically to include if a partner is expected to incur business costs personally, and if they can be Reimbursed for incurring business expenses paid personally. This is not specific to the Vehicle operation or Lease discussion.This is part of LLC business expense, the loss of nonemployee expense deduction, and the TCJA of 2017.

For purposes of reimbursement, there would be receipts, such as printer paper. It's impossible to reimburse for part of a gas fillup, and you cannot prorate how much of which tire got used for personal or business, etc; so the IRS has the provision of Mileage allowance. That covers all operating costs. A partner or an employee using their own vehicle for work would turn in a Mileage Report under what is called An Accountable Plan, to be repaid per IRS mileage rates for the business use. For an employee this is not taxable through payroll as fringe benefit, unless you pay a rate other than the IRS rate. For a partner, this is not allowed unless it is provided for in the LLC documents. That is not a company policy issue; it's in Law. And that is assuming this person was required to use their own vehicle and expected to pay their own costs:

https://www.jdsupra.com/legalnews/are-your-unreimbursed-partner-s-9980145/

If I decide to use my own truck because it is nicer than the one the LLC provides, that would be subject to negotiation, or I would be required to "suck it up" in that case.

The LLC cannot depreciate something they don't own. They cannot pay to operate or repair a personal truck owned by another, unless they are Leasing it with that exclusive right, the same as if the LLC leased it from Ford or Dodge or GM. Well, unless they damage someone else's property, such as, the company Truck backs into an employee's truck. The company repairs both trucks. That's happened to my truck.