Cold light heads represent an inductive load as opposed to a resistive load. Typically an inductive load will have a higher inrush current then a resistive load. Thus the problem that can occur is that the relay in the timer that is responsible for switching the power supply to the lamp can be overloaded by this initial peak demand.
I don't know the power demands for the lamp in your enlarger. I have typically seen the initial inrush current on inductive loads run to six times the operating current in some devices.
What can be done in event the timer is incapable of supplying the necessary current is to install a supplementary higher load capacity relay to carry the load of the lamp and to have the timer lamp outputs utilized as the coil voltage supply for the supplementary relay.
Good luck with your purchase.