I've added the restriction to be bridge, as well as bridge:movable=drawbridge.

https://www.openstreetmap.org/way/35602632

Should the same be applied to the trail?  Most rail trails that I've seen would be permissive of night use, but if this one is extensively signposted that that is illegal, it should probably me mark.  The trail website indicates that the hours for the bridge and trail are the same at 7AM-5PM, which I presume would be about dawn to dusk this time of year.

http://www.tammanytrace.org/index.php/closures