This is a qualitative aspect, so I am not sure if there are ways to reach a precise conclusion, although with regards to the business what they are saying can be quantifiable, like growth, margins etc.
One can look at interviews, conference calls and watch, listen to the management talk. One can understand and get the tone of management from them talking instead of reading about what they said, not that it is reliable, but it gives an idea.
Few questions like unlisted companies doing the same business as the listed business, appointing family members in key positions without them having sufficient qualification or experience, what they do in a particular situation - delayed orders (Mayur), no clarity regarding succession, CEO etc (Cupid), increasing remuneration despite having other options (Avanti), unrelated purchases (Venky’s), frequent auditor changes, RPT, interested about their stock price (Parag I think), poor/nil communication etc.
Few trustworthy points are dividend payout, buybacks, no key persons resigning, good capital allocation, transparency in communication, regular conference calls etc. One can even go by valuations - market trusts the management (Dmart).
These all are subjective and debatable, but gives a vague idea at the least.
The proof out of the pudding is obviously in the eating, and as investors belong to different groups, some stay for long term despite the business not performing for extended periods of time due to their trust, some may think of opportunity cost, some don’t find other opportunities so stay, it depends.
Just my thoughts.