I've never worked with or met SEs (in fact, it looks like the SE PE test was discontinued) with a PE but most states have plenty of MEs (think HVAC design) and EEs (think switchyard or power station design). To your point, yes, it's mostly construction because this field is the one that generally requires PE stamping of documents. As stated in a previous comment, other engineers typically work under what's called an industrial exemption, although there's been some states phasing out these exemptions (https://www.nspe.org/sites/default/files/resources/pdfs/Lead...). If there is an exemption in place, you can typically work as an engineer without a license or without working under somebody with a license. The exact exemption clauses are specific to each individual state's licensing board.
"Every state
exempts from licensure engineers whose practices fit within one or more of five
categories: (1) engineers working under the supervision of a licensed engineer
who takes responsibility for the unlicensed engineer’s work; (2) engineers
employed by public utilities; (3) engineers employed by the federal government;
(4) engineers employed by a state government; and (5) “in-house” engineers
employed by a manufacturing or other business firm (known as the “industrial
exemption”)." [0]
Many states don't differentiate the title of PE based on discipline (although you test with a specialty). If you search in the sos website, you'll notice all are just listed as a "Professional Engineer" license. It's up to the licensee to use professional judgement on whether they are capable of signing off on a specific system (e.g., while a ME may be legally allowed to sign off on an electrical design, they should know better than to do so)
"Every state exempts from licensure engineers whose practices fit within one or more of five categories: (1) engineers working under the supervision of a licensed engineer who takes responsibility for the unlicensed engineer’s work; (2) engineers employed by public utilities; (3) engineers employed by the federal government; (4) engineers employed by a state government; and (5) “in-house” engineers employed by a manufacturing or other business firm (known as the “industrial exemption”)." [0]
Many states don't differentiate the title of PE based on discipline (although you test with a specialty). If you search in the sos website, you'll notice all are just listed as a "Professional Engineer" license. It's up to the licensee to use professional judgement on whether they are capable of signing off on a specific system (e.g., while a ME may be legally allowed to sign off on an electrical design, they should know better than to do so)
[0] https://digitalcommons.liberty.edu/cgi/viewcontent.cgi?artic...