What is the most effective way to improve BGP convergence in the event that a point-to-point link, over which an EBGP session is running, fails?

Lowering the keepalive timer reduces the hold timer expiry window but still requires waiting through multiple missed keepalive intervals before the session is declared down, making it slower than an interface-state-driven mechanism.

EBGP fast external fallover, enabled by default on Cisco IOS, monitors the operational state of the interface over which the EBGP session runs; when that interface goes down the session is torn down immediately without waiting for the hold timer to expire, triggering rapid route withdrawal and reconvergence in milliseconds rather than seconds.

BGP multihop (ebgp-multihop) allows EBGP peering across non-directly connected routers and is unrelated to improving convergence speed when a direct point-to-point link fails.

BGP graceful restart is designed to preserve forwarding state and delay route withdrawal during a BGP speaker reload, which intentionally slows convergence to maintain traffic flow - the opposite of what is needed here.