Here's what the state laws of Texas have to say about it:
SUBCHAPTER G. LICENSE REQUIREMENTS
§ 1001.301. License Required
(a) A person may not engage in the practice of engineering unless the person holds a license issued under this chapter.
(b) Except as provided by Subsection (f), a person may not, unless the person holds a license issued under this chapter, directly or indirectly
use or cause to be used as a professional, business, or commercial identification, title, name, representation, claim, asset, or means of
advantage or benefit any of, or a variation or abbreviation of, the following terms:
(1) “engineer”;
(2) “professional engineer”;
(3) “licensed engineer”;
(4) “registered engineer”;
(5) “registered professional engineer”;
(6) “licensed professional engineer”; or
(7) “engineered.”
(c) Except as provided by Subsection (f), a person may not directly or indirectly use or cause to be used an abbreviation, word, symbol,
slogan, or sign that tends or is likely to create an impression with the public that the person is qualified or authorized to engage in the
practice of engineering unless the person holds a license and is practicing under this chapter.
§ 1001.353. Procedure for Renewal
(c) A person whose license has been expired for more than 90 days but less than two years may renew the license by paying to the Board
the required annual renewal fee, a late renewal fee and any applicable increase in fees as required by Section 1001.206 for each delinquent
year or part of a year.
(d) A person whose license has been expired for two years or more may not renew the license. The person may obtain a new license by
complying with the requirements and procedures, including the examination requirements, for obtaining an original license.
In other words, when your license is expired and is not renewed, you're not a registered engineer, can't call yourself such.
You might also note that the various licensing boards do issue rosters (usually available online) of all currently licensed engineers. If anyone you're ever dealing with decides to look you up on the roster (which is a handy way to verify company and name spelling, by the way), they'll find out right quick your actual status.
You might also note that taking the test(s) is just part of the licensing process. You could, in Texas, get licensed without the tests, and you could conceivably take the test and never get licensed. They're not the same thing.
Most states have similar rules, and most states have their rules online. If in any doubt, call up your state licensing board and ask them.
I would be curious if you still drive with your 30-year-old driving license. I took a test for that, too.