That's a nice, concise, summary Beezerboy.
But 21.183 is " Issue of standard airworthiness certificates for normal, utility, acrobatic, commuter, and transport category aircraft; manned free balloons; and special classes of aircraft." and does not address or require that all things installed in aircraft be identified as "aircraft parts".
An example might be interior equipment such as cabinetry, upholstery, and cigar lighters/accessory-outlets, many of which are automotive/household items and which may be installed upon inspection/field approval/minor-alteration rules.
Short answer to OP, "No." When our aircraft were certificated there were not "TSOs" and therefore none applied. Some regulatorily req'd equipment has been invented since then (ELTs, GPS's, solid-state radios, etc.) and some of those must meet installation/performance requirements defined by their TSO's....and so must meet those standards.
Most items in our aircraft are not req'd to be TSO'd, unless they are "essential" equipment such as req'd equipment (front seat shoulder harnesses installed in aircraft built after 1978(*) such as ELTs. VFR aircraft are not req'd to have TSO'd instrumentation as long as the instruments meet another form of FAA/CAA/Military approval (i.e., AN/NAS/MS).
In other words no matter how good they look, you may not install chineese copies of airspeed/altimetry in certified aircraft, (but you may install them in VFR-only ultralights and homebuilts.) AC 23-21 provides guidance for installing ordinary automotive replacement parts (such as V-belts for you guys operating belt-driven vacuum pumps), voltage regulators, generator/starter brushes, primary engine instrumentation, etc..
A cigar lighter is not req'd equipment, but it (and similar after-market items) must be installed IAW (in accordance with) applicable FARs/Advisory Circulars. (such as FAR 43.13(a)/(b). Paragraph (b) states: "Each person maintaining or altering, or performing preventive maintenance, shall do that work in such a manner
and use materials of such a quality, that the condition of the aircraft, airframe, aircraft engine, propeller, or appliance worked on will be at least equal to its original or properly altered condition (with regard to aerodynamic function, structural strength, resistance to vibration and deterioration, and other qualities affecting airworthiness)."
The word "materials" applies to parts. One method to comply with that qualtity-requirement is to have mfr'r assurances such as TSO's, PMA's, or other standard such as AN/NAS etc.. However many parts such as found in our aircraft are automotive in origin. (I am thinking here of such items as mechanical fuel-quantity gauges, oil temperature gauges, vibrating-point voltage regulators,
cigar-lighters....etc.)
We have a Member whose AP/IA insisted that his cigar lighter MUST be official "Cessna". He searched high and low and "lucked out" finding an N.O.S. one still in it's original, tattered, Cessna-envelope. (One can only imagine what Cessna might demand of such an item these days.)
As picky as I have been considered by many,.... I think that IA/AP stance is particularly assinine. It is similar to those who insist that light-bulbs/lamps must only be "GE", etc. (I wonder if any of those authoritarians have ever noticed that some lamps in the Cessna parts catalog were originally specified as "Mazda".)
The problem here is , ...you can lead a horse to water but you cannot make him drink. You can hand your IA/AP a cigar lighter...you may even hand him a ceramic-and-stainless steel one from a million-dollar yacht much better in quality than anything Cessna ever installed......but you cannot "make" your IA/AP installit unless he agrees it's applicable to aircraft use.
HE has to keep his certificates in order to earn a living and HIS FAA inspector has likely given him a personal opinion or two that he uses as a guide as to what he may/may not install in aircraft.
AS for an engine-monitor installed in addition to the other instrumentation already installed to meet requirements.....that is auxilliary equipment and must not interfere with the required equipment, but otherwise if it and the installation meets the quality standards for aircraft (FAR 43.13(b)....then it is legal to do so. IMO