True Runes have a will of their own to shift from one place to another but since they store fragments of the future they always need a triger move on, that is the Bearer's role or fate.
1-Rune of Punishment, needs someone to Hitchhike. lol
2-Rune of Life and Death, we don't know cause Windy followed it for many many many (Thats 300) years. I think it can travel on its own unlike the Rune of Punishment which needs a host.
3-The Night Rune, ask the Crazy Sword. No the Rune actually traveled with numerous wielders, so yeah it didn't stay in one location.
4-The Gate Rune, ask Leknaat.
5-Dragon Rune, unknown due to the Dragon connection.
6-The Beast Rune, left Harmonia and ended in the Highland Palace.
7-True Fire Rune, waited its fate in the Grasslands. Can it fly somewhere? I think yes, see True Wind Rune and True Earth Rune.
8-True Wind Rune, (Albert's testimony in S3 manga) the Rune left the Ceremonial Site after the battle Between Hugo, Chris, Geddeo and Sasarai against Luc. Maybe all the Elemental Runes can do this too.
9-True Earth Rune, well when its seal was broken in the Ceremonial Site Sasarai was able to draw it back to him. Yup unknown.
10-True Water Rune, Ask Wyatt.
11-True Lightning Rune, unknown.
12-Sun Rune, for some reason it loves the south. Drying the Ancient Armes and then wait for Falena to be established.
13-Rune of Change, 100% yes due to the Sindar's nature in traveling from on place to another. Though Eternal City can ruin this theory.
14-Circle Rune, ask Hiky.
15-Rune of the Beginning, separation complex and its unkown.
16-Blue Moon Rune, Theft, also unkown.
17-Sovereign Rune, family heirloom still unkown.
18-Eightfold Rune, very crazy wielder with a disturbed childhood, but yeah he ran away from Pesmerga.....??