I'm definitely in the camp of not getting a signature. I recommend sending a cover letter with the GFE outlining what you need (verification, deposit) to proceed. Also ask the customer to contact the loan if they wish to proceed.
If they call/stop in, bring in verifications or a deposit, you have evidence of their intention to proceed.
You have to obtain the customer's acknowledgement of their intent to proceed
I technically disagree. The borrower's don't have to sign anything. Your statement implies that they do. Here's the relevant FAQs on this topic:
After a loan applicant both receives a GFE and indicates an intention to proceed with the loan covered by the GFE, the loan originator may collect fees beyond the cost of a credit report for origination-related services. [RESPA FAQ – GFE General #10]
Acknowledgement of receipt of a GFE, by itself, does not constitute an expression of an intention to proceed with the loan covered by the GFE. [RESPA FAQ – GFE General #28]