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Please fill in a phone number where you can be reached during the daytime.
Literal
Daytime [even-でも] contact [subject-が] goes-through phone-number [object-を] honorific-fill-in-please.
A stock phrase from contact forms. 連絡がつく ('contact goes through, contact can be made') is an idiomatic fixed phrase — the intransitive verb つく here means 'to be established, come through'. The honorific template お/ご + verb-stem + ください appears in ご記入ください — this is the keigo request form using the sino-Japanese prefix ご for compounds of Chinese origin. The set phrase 昼間でも連絡がつく ('reachable even during the day') assumes daytime is when most people are unreachable due to work.