Siva, who is Pure Awareness
Transcending thought, is only known
To seers heroic who with minds
Extinct abide thought-free within
The heart, and not to those whose minds
Are still engaged in thought.

Guru Vachaka Kovai, Verse 1238

(Tom: ie. Liberation is not known to those who are still engaged in thought. One must abide with ‘minds extinct’ and ‘thought-free’)

In response to the above quote from Sri Ramana Maharshi, the following question was asked:

Questioner: Thoughts just appear don’t they? Do they ever stop? Is it not the recognition of the contents thoughts as fiction which is being talked about?

Tom: Yes, this is a point that I have often heard. However thoughts must cease for the Eternal to be truly perceived. Otherwise we remain entrapped in this Maya-Illusion.

Your point about thoughts remaining but being perceived as being false is a common ego-preservation strategy for the ego that seeks its own continuance and seeks to avoid the practice that leads to its demise.

This is why Sri Ramana makes the point about thoughts ending again and again.

The notion that thoughts cannot end is a belief and another ego-preservation strategy. I encourage you to explore the various quotes here, best wishes