Is there a way to register a deposit made as a sale? For instance, Eventbrite auto-deposits money in my bank after I teach a class. How do I record this as a sale?

Use a,Sales Receipt and post the inherent payment directly to banking. "+" Customers, Sales Receipt.

If you connected your bank to review feeds this will present a green match to accept unless eventbrite holds back an unknown fee to be calculated later. In that case, post the sales receipt to Undeposited Funds, create a Deposit and deduct the fees as a processing expense

Sarcasm to follow:

Actually, though, the way Danny Devito describes it in the new ads, if you have signed up for QuickBooks you don't have to do another (expletive deleted) thing. It's already done for you without one iota of you lifting an eyebrow let alone a finger. By the time you greet the next student your taxes are done, isn't that wonderful? Just in the time it takes you to read this silly message you made $100

My business uses Eventbrite (EB) for ticketing and has for a couple years and dozens of events.  Here are my recommendations. BTW we pass the fees throught to the customer and the following explanation is based upon this setup.

Create a new customer "Eventbrite" and for each event create a new job under that customer name. In your general ledger create an income account like "ticket sales" or something else appropriate. In your item list create an item linked to the income account "ticket sales". Are tickets subject to sales tax in your jurisdiction? Be sure to include this in the customer profile. Create a "service" item  titled "EBreserve" tied to a GL account like "other income" . This is only a temporay holding account because this ticket platform holds back money (roughly 7-10%) until about 7 days after the event concludes and you want to account for that receivable somehow. I do not like carrying it like a typical receivable due to the very extended time sales preceed the event (months) and the tickets may be refunded or event canceled. That's why I use "other income" for the reserve. I'd like to get a CPA's thought on this.

As you sell tickets, every week EB will EFT deposit funds in your bank account. Create an invoice with the item ticket sales and in quantity put number of tickets sold to date. On the second line of the invoice adjust "EB reserve" amount to "zero-out" the account after taking in account the payout that week. "Receive payments" and pay the invoice. The balance should be zero. When sales taxes are involved you have to work with pre-tax amounts as QB adds taxes at the bottom. Just divide the the payout by 1+ the decimal tax rate e.g. 1.065 for 6.5% tax.

There is another tricky part you have to deal with. Eventbrite charges the customer sales tax on all the fees but in my jurisdiction these services are not taxable. So we always end up with a few extra dollars which have to be accounted for. After the event is concluded and the tickets are all sold I post the total number of paid tickets on the invoice. There will be a small difference between totaly EB payouts and the total sales. This small income is the tax EB levies on the customer's service fees. If there are say $6 fees on a ticket, the tax rate is 6.5%  this amounts to $0.39 of miscellaneous income. You have to account for this. You can use the EB reserve item or create another item just for this adjustment. At the end only one invoice is necessary for each event unless your jurisdiction sales tax rate changes during ticket sales. In that case I create one invoice for each tax rate and allocate tickets accordingly.