Does anyone besides Google "own" this Gmail account? An email's author retains the copyright, but effectively issues irrevocable licenses when sending the email. But afaik Google own the account itself.
Case 1. Do you need access to the account's contents? If so, you are screwed. Google does not hand over accounts easily. For all Google knows, you might be doing all manor of illegal or immoral things, like exposing a whistle blower, attacking a critic, etc. You could earn yourselves a dishonorable mention on Chilling Effects or Google's Transparency Report for even asking.
Google fought China over Gmail hacking. Google's Transparency Report probably makes the CIA and NSA nervous. Google refuses 7% of law enforcement requests for user data in the U.S. In Singapore, Google refuses fully one quarter of government requests for user data. Isn't happening man.
Case 2. Do you merely need the account terminated? If so, you might convince Google that the account violates their terms of service. I'd consider this too risky myself because they might still post your emails to Chilling Effects. You might be trying to silence a critic after all.
A priori, you're concerned with the ex-employee sending official looking emails, but the employee is concerned with receiving emails from personal correspondences who know that email address. If so, ask him to create another gmail account, forward his emails form this one to that one, so no emails come from this account.
If he still says no, you could search Gmail's Terms of Service for any violations. If you find one, you must still take care when contacting Google. Tell them you just want the account renamed or closed with forwarding to another account. Attach his letter of resignation and post employment correspondences. If they see he left by choice, you'll look less like you're trying to silence a whistle blower or critic.
Just remember that a lawyer cannot help you if a Google search for your company shows this dispute with an ex-employee over their effectively personal email address.