Can I compare the peaks of a GAM between two groups?

I fit a hierarchical generalised additive model with mgcv in R to show the relationship between Common Nighthawk (bird) vocalizations and sun angle. I used separate smoother for sites with artificial light at night (ALAN) and sites without ALAN. I want to compare the sun angle at which peak vocal activity occurs for sites with ALAN v. sites without. How can I estimate the difference in the sun angle of peak vocal activity between these two groups of sites and the associated confidence intervals?