@BigRedConsulting 

"QuickBooks Desktop doesn't do that.

With QB Desktop cash basis reporting, prepayment checks applied A/P Bills and customer prepayments applied to A/R Invoices are not recognized until the Bill or Invoice date.

Also, any unapplied amounts for both A/R and A/P payments will not show up on a cash basis P&L - ever."

Additionally, transaction that don't involve any cash can create cash basis events. For example, if you include both sales of new items and the return of an item on an invoice, that will create a cash basis event on the invoice date - even when no payment is received."

Why are you referencing QB Desktop?  This thread is about QB Online and Online handles these transactions differently than Desktop.  QB Online posts A/R payments received prior to an invoice to 'Unapplied Cash Payment Income' and posts A/P payments made prior to the bill date to ‘Unapplied Cash Payment Expense’ on cash basis. No cash basis event is posted in QB Online when you sell new items and return an item.

"Yea. But how do you know that cash received on deposit for some future job will become income until it's applied to something - like an invoice - in the future? How do you know if the money is "received as gross income"?"

It’s the user’s responsibility to record the prepayment accurately regardless. Invoice, deposit, sales receipt, whatever. It’s no mystery in the OP’s case what the payment is for – it’s a prepayment for a future service and the IRS is clear that it is income when received on cash basis.

Per the IRS: (link here )
Prepaid income. Prepaid income, such as compensation for future services, is generally included in your income in the year you receive it. However, if you use an accrual method of accounting, you can defer prepaid income you receive for services to be performed before the end of the next tax year.

The word “generally” is there because there are some exceptions for crop insurance, disaster payments, livestock loss, and a couple of others.

"For example, if the eventual invoice includes sales taxes, other taxes, and other licensing fees or permits, which are paid for and billed to the customer, that's not income. Those fees might routinely make up 20 - 30% of the eventual sale, depending. As I think about this, the prepayment itself may be made to secure the permits and pay other fees. In this case, I expect, the business will know that the deposit on account is not "received as gross income"."

Have you worked as an accountant (financial or tax) or as a bookkeeper? This is cash basis we’re discussing so, yes, it’s income (gross income as the IRS refers to it). It can’t be anything else. If you incur expenses on behalf of your customer and bill them for those expenses, you better record it as income otherwise you’ll deduct the fees as expenses and not have the offsetting income, thereby understating your net (and therefore taxable) income. The IRS frowns on taxpayers understating their taxable income.