Halogen may require more amps from the alternator and different guage wiring. The dimness is from a bad load on the system or dirty connectors and should be checked. You may simply have dirty engine and body ground connections, a weak alternator, faulty relay or a poor battery. A 1966 Mustang
shop manual and an ohm meter can take you through what to check. A bad electrical system will only making the expense of putting in halogen lights worse.
Try disconnecting and wire brush cleaning all the major connections: battery, engine grounds(especially to firewall), relay connections, etc. Good luck