Caped Carousers RuneScape's oldest Quest Cape clan

Amy's Anachronia Advice - Agility

The rewards of double-surge and double-escape are (rather accurately) suggestive of the fact that almost any movement ability will come in handy whilst playing various bits of content on the island.

The mobile perk - it halves the cooldown of them all - is also useful.
It requires one weapon or armour gizmo, and I suggest 1 Subtle component + 4 Dextrous components.

For anyone trying to do the agility couse in under 7 minutes, I found this guide helpful:

Courtesy of Amaterasu Mi, last updated Oct. 14th 2019