First only puthujjanas who are materialists care about the brain.
Second, the word mindful for sati or satipatthana is really used by people lacking vocabulary.
Same situation for the word mind, but even worse, since is there no mind in pali, but a declination into 3 words. THere is ''citta'', there is ''mano'' and there are the 6 ''Vinnana'', ie the consciousness aggregate (viññāṇakkhandha).
THe wandering of the mind is the ''papanca'' of the mano.
Third, the way to be concentrated on something is to be relaxed and have joy, piti. Once you are concentrated, you have joy and once you have joy your citta is not dispersed to the point of not being disturbed by little pains, sounds, or worries . In other words, you cannot be concentrated without having joy.
Your fantasy of naggering the person filled with papanca and struggling to reduce the papanca has nothing to do with this joy.
"Furthermore, the disciple of the noble ones is endowed with verified confidence in the Dhamma... verified confidence in the Sangha... virtues that are appealing to the noble ones: untorn, unbroken, unspotted, unsplattered, liberating, praised by the wise, untarnished, leading to concentration. Not content with those virtues pleasing to the noble ones, he exerts himself further in solitude by day or seclusion by night. For him, living thus heedfully, joy arises. In one who has joy, rapture arises. In one who has rapture, the body becomes serene. When the body is serene, one feels pleasure. Feeling pleasure, the mind becomes centered. When the mind is centered, phenomena become manifest. When phenomena are manifest, he is reckoned as one who dwells heedfully.
Since you care about papanca, here is the method to avoid it: first you become a disciple, you do satipaṭṭhānaṃ , you have confidence in the buddha and when you are around people you do satipaṭṭhānaṃ , confidence in the buddha and you are ''nice guy'' which means you show''Khantiyā, avihiṃsāya, mettacittatāya, anudayatāya'' ie patience, harmlessness, friendliness and sympathy. https://suttacentral.net/sn47.19/en/bodhi
THen you go to a place alone. Then your mano has Pīti, then your body has passambhati, then has sukhaṃ vediyati, which is pleasant vedana, then the citta has sukhha, and once it has sukkha it has samādhi, which is centered or ''not dispersed''. Once you live like that, you are a person who ''lives diligently'' and ''knows phenomena when they manifest''.