From 31.3121(a)-1(d):
(d) Generally the basis upon which the remuneration is paid is immaterial in determining whether the remuneration constitutes wages. Thus, it may be paid on the basis of piecework, or a percentage of profits; and it may be paid hourly, daily, weekly, monthly, or annually. See, however, § 31.3121(a)(8)-1 which relates to the treatment of cash remuneration computed on a time basis for agricultural labor.
Most of 3121(a) is devoted to the idea of saying, "it doesn't matter what you call the payment, treat it as 'wages'". Specific to this question, I think the "percentage of profits" will sweep up self-employment income.
One fun fact I found:
31.3121(b)(17)-1 Services in employ of Communist organization.
The term “employment” does not include services performed in the employ of any organization in any calendar quarter beginning after June 30, 1956, and during any part of which such organization is registered, or there is in effect a final order of the Subversive Activities Control Board requiring such organization to register, under the Internal Security Act of 1950 (50 U.S.C. 781 et seq.), as amended, as a Communist-action organization, a Communist-front organization, or a Communist-infiltrated organization.
For all those who would say, that's not a thing anymore, you would be correct to the extent that the Board was abandoned after Nixon budgeted $0 to it in 1973(?). However, it has never been dealt with legislatively and is technically still in existence. I wonder if there are any of the registered organizations that still exist whose members should not be recognizing wages???