ticken
to tick
To produce the regular, quiet sound that is typical of a clock or an alarm clock.
Die alte Standuhr im Flur tickt sehr laut.
The old grandfather clock in the hallway ticks very loudly.

to tick / work
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to tick
To produce the regular, quiet sound that is typical of a clock or an alarm clock.
Die alte Standuhr im Flur tickt sehr laut.
The old grandfather clock in the hallway ticks very loudly.

The meaning of 'ticken' (to tick) depends heavily on the subject. If the subject is a clock, it refers to the sound. If the subject is a person, the colloquial meaning 'to think' or 'to function' is meant.
Meine Armbanduhr tickt nicht mehr, die Batterie ist wohl leer.
My watch isn't ticking anymore; the battery is probably dead.
The use of 'ticken' (to tick) for the way a person thinks or functions is typical of colloquial speech. You often hear it in informal conversations.
Sag mal, wie tickt dein neuer Kollege eigentlich so?
Tell me, what is your new colleague actually like?
The phrase 'nicht richtig ticken' (to not be right in the head) is a fixed expression. It is always used in this form to express that someone is behaving unreasonably or seems to be crazy.
Du willst bei diesem Gewitter wandern gehen? Du tickst doch nicht richtig!
You want to go hiking in this thunderstorm? You must not be right in the head!
In the colloquial meaning, 'ticken' (to tick) is often used in subordinate clauses with the question word 'wie' (how) to question or describe the way someone thinks or acts.
Es ist schwer zu verstehen, wie diese Organisation tickt.
It is hard to understand how this organization ticks.
to think
'denken' and 'ticken' can both have to do with a person’s inner nature. 'Denken' is the normal word when someone has thoughts, thinks about something, or has an opinion. 'Ticken' is colloquial and describes more how someone thinks, feels, or reacts overall. For example, people say: 'Ich weiß, wie er tickt.' (I know how he ticks.) This does not mean just one individual thought, but his way of being. Learners may confuse the words because 'ticken' in this sense also has to do with thinking. For normal thoughts and opinions, use 'denken'; for a person’s individual way of being, 'ticken' fits.

Nach ein paar Wochen im Team weiß Sofia, wie ihre neue Chefin tickt.
After a few weeks on the team, Sofia knows how her new boss ticks.
Mein Kollege denkt, dass der Termin am Montag zu früh ist.
My colleague thinks that the appointment on Monday is too early.