I won't try to answer whether the law is constitutional as that's not a subject I am well versed in, and has been addressed by others.
Note: Tennessee law allows "adult entertainment". But this amendment has tightened it down to where some of them can be performed. The amendment specifically bars it from public property and locations that may allow minors easy access:
Obscenity and Pornography - As introduced, creates an offense for a person who engages in an adult cabaret performance on public property or in a location where the adult cabaret performance could be viewed by a person who is not an adult. - Amends TCA Title 7, Chapter 51, Part 14.
What does the amended law say?
AMENDMENT #1 rewrites this bill and creates an offense for a person who engages in adult cabaret entertainment on public property or in a location where the adult cabaret entertainment could be viewed by a person who is not an adult. This amendment defines "adult cabaret entertainment" as adult-oriented performances that are harmful to minors, as such term is defined under present law; feature go-go dancers, exotic dancers, strippers, male or female impersonators, or similar entertainers; and include a single performance or multiple performances by an entertainer. An "entertainer" means a person who provides:
(1) Entertainment within an adult-oriented establishment, regardless of whether a fee is charged or accepted for entertainment and regardless of whether entertainment is provided as an employee, escort, or an independent contractor; or
(2) Adult cabaret entertainment, regardless of whether a fee is charged or accepted for entertainment and regardless of whether entertainment is provided as an employee or an independent contractor.
Present law defines "harmful to minors" as that quality of any description or representation, in whatever form, of nudity, sexual excitement, sexual conduct, excess violence, or sadomasochistic abuse when the matter or performance:
(1) Would be found by the average person applying contemporary community standards to appeal predominantly to the prurient, shameful, or morbid interests of minors;
(2) Is patently offensive to prevailing standards in the adult community as a whole with respect to what is suitable for minors; and
(3) Taken as a whole lacks serious literary, artistic, political, or scientific values for minors.
How do they define, specifically, what it means to be dressed in drag?
They don't. They instead focus more on the behaviour of adult entertainers - of a "male or female impersonators" performing outside a permitted environment, that maybe accessible to minors, for a very specific purpose (adult entertainment).
Let's say we're clear on whether someone is male or not, now what does it mean, specifically, what female clothing is?
That is irrelevant as the law specifies that it only applies to an adult entertainer impersonating the opposite gender, behaving in a sexually suggestive manner, as part of some adult performance, outside of a permitted avenue that may be accessible to minors. A prosecutor trying to prosecute a man who dressed in an obvious women's clothing will still need to prove that the accused is an adult entertainer, was trying to impersonate a women in a sexually suggestive manner to arouse the public sexually as part of some public adult performance (outside those permitted by law), without any regards to minors who may have been easily exposed to his act.
But yes, the law has enough ambiguity that can allow multiple interpretations about a situation that can be easy to misrepresent to a jury.
If the pope visits Tennessee, will he be deemed guilty of dressing in drag?
No. Not unless he suddenly claims to be an adult entertainer and also pretends to be a female while doing something sexually suggestive in a public place where adult entertainment are prohibited, to sexually arouse the public disregarding if minors can see his act.
Will women wearing slacks be deemed guilty of dressing in drag?
No. Not unless they claim to be adult entertainers while pretending to be a man and doing something sexually suggestive in a public place where adult entertainment are prohibited, to sexually arouse the public while disregarding if minors can see their act.
I can't possibly see how any meaningful legal specificity can be in such a law and for it to possibly be constitutional.
Even if the law is flawed, the amendment and final version of it does provide a thin shield to protect it from judicial review - that it is a law to protect minors from exposure to pornographic acts accessible to adults. And it also provide a big stick to politically attack those who oppose it - namely, it allows casting aspersions on those who oppose the law as suspected paedophiles who don't seem to care about the well-being of children the law attempts to protect.
Note though that in a good judicial system, ambiguous laws tend to get defined more and more narrowly, and thus the set of judicial precedents on the law tend to dictate more how it is enforced in the court, than based on the original letter of the law. Also, ambiguous laws tend to be easier to kick to a higher court for a judicial review.