Always prioritize the flesh tones. Let everything else fall where it may. Get the flesh tones correct for most video content and on a Mit you'll have blue-green diminish unless you correct for the colorations some other way, because Mit has strong red push. But on a Tosh the red push is not nearly as strong. So getting the flesh tones correct by eye should give your pic an awesome color paradigm.
Just don't trust the blue filter/isolation test,
because if there is any red push, it will get your blues correct but will overaccentuate the reds in your flesh tones, compromising your suspension of disbelief and blowing your hypnotic trance. Better to do the flesh tones by eye on most channels/video material, and trim where needed on that occasional video material that is not actually correct.
On a Tosh, chances are that not just lens cleaning will need it, in your optics cleaning op. Other surfaces will most likely be involved.
But don't take any chances on cleaning it the wrong way, which could cause permanent damage. Call me and get it from the horse's mouth, from someone who's been there countless times by now, in my calibrations all over the country.
Those 6 additional surfaces in the deeper optics category comprise more than half of the 10 surfaces that may need cleaning of the 28 total, depending on the brand. Not doing those additional 6 surfaces if they need it will keep your set limited on the inkiness of its blacks, which CRT still does the best at - second only to OLED, which is not really here yet. Yes the blackening of the optical cavity makes a difference and should be done as well, but not nearly as much difference as the optics cleaning makes.
Here's the results of having all 28 surfaces in your light path crystal clear again, on a Pioneer set where all 10 in question needed cleaning. Mit seals their lenses to their CRT coolant covers properly whereas other brands do not, Tosh most likely being one, depending on the model. Some did and some did not. This means that on brands other than Mit, 10 of the 28 surfaces need cleaning on other brands, to Mit's 4.
The importance of this step cannot be overly stressed. It is ESSENTIAL!
It usually takes about an hour if you're a quick study, less if you are long experienced like I am. If you are totally inexperienced at it, it could take a little longer. But by the end of the day you'll have your new-looking set back again, like the day you bought it.
After (same day and from then on!):