What are we talking about?
This is probably a usage question, because to me "timber" is distinct from light-frame "wood" design. The resources everybody is pointing at are light-frame references, although Breyer touches on heavier "heavy timber" timber design elements (glulams), this is the building code stuff, the 6x8 beams and 6x6 column minimum sizes that are big enough to withstand a fire.
When it comes to the "timber frame" more ornamental stuff like mortise and tenon structures that are more commonly seen in England and some showier wood structures in the U.S. The connections are usually wood peg, or something similar, are more esoteric and the domain of the Timber Frame Education Council. And "Mass timber" (which sounds like cross-laminated timber to me), is a different creature yet again. So there's three things here, if you ask me. Not sure which one the OP wants to know about. So I can't go too far on advice there.
Employee or not?
With regards to the you'd have to be an employee comment, in my opinion this is not correct. Sure, that's more conventionally done. The insurance in the event of a lawsuit or worse is probably a lot happier that way as well, but an engineer of record ( design firm ) cannot hand a wood project or a timber project to an unskilled inexperienced engineer or engineer in training or a "structural enthusiast" who's interested in learning the basics by doing, they need to meet the requirements of responsible charge and direct supervision, (unless the outside engineer has demonstrated competency and will stamp the final design, I suppose) and this can be accomplished without being an employee.
The insurance for O&E might have complaints or clauses about this down the road, should a problem (meaning lawsuit) appear, but that sort of thing I feel is surmountable, because ultimately it is on the design professional (an employee of the firm, who is stamping the final design) who is in responsible charge, i.e. the engineer of record, and if they stamp the drawing, they are effectively certifying the work is correctly done to their standard of care.
They are responsible for reviewing all the work by a subordinate (regardless of employment status) as if they did it themselves, are required to be involved in the process beginning to end (framing selection, bearing points, choice of floor trusses, I-joists, prefabricated rafters, design criteria like snow load, live loads, dead loads, etc., shop drawing review, site inspections, etc). This does not mean you have to hold their hand the entire time or even walk them through every calculation, you could use the same approach that's involved in becoming a successor engineer, i.e. from their "final" design, you perform all the necessary calculations to confirm or revise their design accordingly, complete load path, etc. You could (should/must) do the same thing if somebody asks you to "plan stamp" their work and they've not been anywhere near your locus of control, not under your direct supervision, are completely unknown to you as to their skills or qualifications.
Ultimately, there is NO difference between having an EIT, a person without an EIT who is familiar with how to perform the calculations (mathematician, accountant, wife or child, engineering student, paid or unpaid intern from the local university, paid by the university, out-of-work Maytag repairman, whatever), and a fellow professional engineer who just happens to not have a license in the state where the project is going to be constructed. As the Engineer of record, the requirements are EXACTLY the same. Direct supervision and responsible charge.
Some/many/most design offices do NOT follow these rules and when one P.E. does a design and another is going to stamp it, there is probably about zero review because "they know the guy". This will NOT be a satisfactory response to any board of professional engineers if there is a problem with the project (collapse, complaint from a contractor or city building official). I'd expect nobody is going to admit they did zero review of another engineer's work, but if they didn't do any review then there won't be any calculations in the file, will there?
Any time I was doing a project "under" another engineer's license, they nitpicked the heck out of the work and did their own review of the design, independently, even if I have my own license. I don't know the point of that, either they were trying to decide I could handle it myself for the next one, they wanted their name on the final project, or that was the way they intended to operate going forward. As a specific example, we had a high school addition where the architect was going back and forth on the size of the building, so I was told to design the open web steel roof joists as if they were two feet longer than the current design, and to design for a ballasted roof. On review before that engineer stamped the project, I got asked about the joist designs being "too heavy", because the joist designs were never trimmed to the correct lengths, so the review was that detailed (I forget if the joists were designed too long and the ballasted roof wasn't ultimately done). (We were both licensed in the state in question).
I've worked "under" another engineer who didn't review much of anything (we were both licensed in the state in question) and had to basically chain them down to a desk and force them to go through the design in front of me, interrupt them periodically to get them to supervise the design process. send email after email to drag them to the table, etc, force them to confirm location of bearing walls, etc. That did not last that long. I found their approach intolerable and irresponsible.
([link file:///C:/Users/expat/Downloads/007.0-Change-of-Architect-Engineer-of-Record-ADA3.pdf]City of Coral Gables information[/url], which references the Florida code)
While this is not a casual process, and requires deliberate thought, nowhere in there is an employee relationship an actual requirement that I've seen.