Clarify hair when needed and that is determined by how the hair looks and behaves.
Clarify when your hair feels or looks: dull, heavy and dry, hard to manage, more tangly, and in general more difficult to deal with, when combing or styling. There is no difference in terms of needing to clarify, whether a product contains silicone or not. All conditioners cause build-up on the hair and many shampoos and soaps available today do as well. They are designed to do so, in response to consumer demand for more: conditioning, hair volume, or styling control. All styling aids and thermal protectants cause build-up on hair too. These products keep depositing coatings on the hair every time they are used and not all of the coatings are removed when the hair is washed.
The hair shafts become overloaded and clarifying, or removing the coatings with a product designed or chosen to do so is the only way to "reset" the condition of the hair. A shampoo with minimal extras can help remove product residues but in most cases, that will take time and you need to stop using the products that cause the residues.
The only ways to clarify hair from build-up I know of are clarifying shampoos, or baking soda in water (fully dissolve the baking soda in water so that it is not abrasive) and immediately follow it with an acidic rinse that is well diluted, like vinegar or lemon juice or citric acid.
Baking soda (sodium bicarbonate) has a few advantages for clarifying hair as opposed to clarifying shampoos. It is cheap, easy to obtain, and you control how strong the solution is or is not, by the amount of baking soda used to the amount of water. A too strong solution can leave hair dry. An acidic rinse like those mentioned has a lower pH than most conditioners. Closing the cuticles immediately after using baking soda is important, whether you condition the hair after that or not, to prevent tangling and stress on the hair.
A clarifying shampoo is a shampoo with strong cleanser(s). It does not have to be sodium lauryl sulfate. It can be ammonium lauryl sulfate, or sodium laureth sulfate, or sulfate-free cleansers in high enough concentrations. The best clarifying shampoos contain almost nothing else, no polymers, no botanicals, no waxy ingredients like cetyl alchohol and no liquid waxes like jojoba oil, or shea butter. The problem with such extras in a clarifying shampoo is that not only is the shampoo less effective at removing other residues, it can leave residues of its own behind and that means clarifying can be needed more often.
This is an example only of a clarifying shampoo, with almost nothing else. Colour add by me.
"Water, Amino Methyl Propanol, Ammonium Lauryl Sulfate, Cocamide DEA, Sodium Chloride, Fragrance, Sodium Phosphate, Disodium Phosphate, Ammonium Xylene Sulfonate, EDTA (Ethylenediamine-Tetra-Acetic Acid), Benzophenone 2, D&C Green 8, Methylchloroisothiazolinone, FD&C Blue 1 (CI 42090)"
The Amino Methyl Propanol is a pH adjuster and the EDTA is a chelating agent to help with hard water. Combinations of ingredients with the cleanser(s) in such shampoos are designed to remove residues or build-up efficiently.
The above is about product build-up.
To remove soap scum use one of the above acidic rinses well diluted. Acidic rinses made too strong can be drying. Pure citric acid can be very strong and much less is needed for a rinse. When diluting any acidic rinse, especially if you are using a pure acid like citric acid, it is a good idea to use pH papers to measure the pH of the final result. A pH of about 4.5 - 5 is very good for hair and skin. A pH below 3.5 can damage hair.
To remove mineral build-up use one of the acidic rinses (lemon juice chelates metals like iron as does pure citric acid), or club soda, or a chelating shampoo and some chelating shampoos but very few, can reduce product build-up. A chelating shampoo is not in general designed to clarify hair, just bind metals and remove them from the hair when the shampoo is rinsed out.
Club soda does not chelate. It is acidic and helps break up minerals on the hair, neutalizes chlorine and can remove mineral deposits like calcium. The small amount of baking soda in club soda is part of the buffering system only, which stabilizes the pH of club soda to be hair and skin friendly, at about pH 5, which means that it needs no diluting. The fizz is harmless. Club soda does not need to be used flat.
Since the purpose of an acidic rinse is the removal of soap scum and hard water minerals, as well as to re-acidify the hair after alkaline products and close hair cuticles, I do not recommend leaving acidic rinses in the hair, diluted, or as with club soda not diluted.
EDTA in a shampoo chelates calcium and magnesium. A vinegar rinse, although it does not chelate, or club soda can also remove calcium and magnesium deposits from hair.