The sign of the sundial was a precursor to the main event: during the the night 185,000 soldiers of the Assyrian army became dead corpses. The Assyrian king fled to Damascus where he was killed by his own children.
Hezekiah Superstar
I Didn’t Confer With Flesh and Blood
After Paul's conversion on the Damascus road he spent three years in Damascus and Arabia being taught, by the Holy Spirit, the doctrine which he would preach, teach and eventually write.
Jerusalem to Damascus
Given that a walking route 2,000 years ago may be much more direct than a modern driving route, and consider that Saul was young, fit and motivated, plus may have walked more than 8 hours in a day, then the journey probably took 5 days.