The 60ct1 uses a nicad battery, nicads will often not take a charge if they are fully drained and left in that state for a long period. The charger port is on the battery holder on the opposite side from where the strobe plugs in. I looks to me to be a proprietary connection using a 120/7 volt AC transformer.
charger: Metz Typ728 part number 0000728
battery: Metz NC-Akku 60-39 000060393