Yamadera opening hours?

Can you climb up to Yamadera at any time? I know the temples and shops have business hours but is there a gate/entrance that prevents you from doing the climb early in the morning or towards the evening?

It seems that you pay the entrance fee at the temple gate, so you can only go beyond the entrance time.
https://www.rissyakuji.jp/index.html
From December to the end of March, the reception starts at 8:30, the reception ends at 15:00, and the closing time is 16:00.
After April, it will probably be from 8:00 to 17:00.
https://www.rissyakuji.jp/index.html
https://www.yamaderakankou.com/pamphlet/index.html
https://www.yamaderakankou.com/pamphlet/pdf/pam_2019pink.pdf

I remember there was a gate. So no. This is a temple and like most things ther temples it has closed hours. The monks want to sleep.

Makes sense, I had the option of going in a loop through Yamagata from Sendai so I'll make plans on visiting in the morning then.

I can confirm that it does have gates and specific opening hours.

Check train times carefully as they are few and far between

Has anyone been there recently and know of luggage storage options in the station or surrounding area?

There seems to be a large locker in front of the toilet at the station.
Also, in front of the station, if you want to buy souvenirs, there seems to be a store that will store your luggage.
https://coinlocker-shiori.com/yamadera-station/