An enquiry arrives at twenty to four in the morning. Somebody could not sleep, went looking, found you, and filled in the form. They were ready to buy.
Your first reply goes out at eleven the next morning, seven hours later. By then they have messaged two other firms, one of them has answered, and the meeting is booked. You never find out that any of it happened, because a lead that goes elsewhere does not write to tell you so.
This is not a staffing problem, and you will not fix it by asking people to check their phones in the evening. They will do it for two weeks. What you have is a coverage problem, and coverage is one of the few things software handles better than a person.
The job an after-hours responder needs to do is small. Acknowledge the enquiry and say that a person will follow up. Answer a question it can answer from material you wrote yourself. Offer two specific times. Done properly, that closes the gap that was costing you the lead.
What it must not do matters more. It should never quote a price, commit to a delivery date, or agree to anything about scope. It should also say plainly that it is automated, because a customer who works out halfway through that your helpful colleague was software will remember that for longer than they remember the fast reply.
Someone reads every overnight conversation properly the next morning, not a skim over coffee. That rule is what keeps the rest of it safe, and it is the first thing a comfortable team lets slide.
If you get four enquiries a month, do not build any of this. Check your phone. An after-hours responder earns its cost at volume, and below that it is a toy that makes a small business look like a call centre.
There is a boring test that settles it. Count the enquiries that arrive outside working hours over one month, then count how many of those turned into a conversation. If the two numbers are close, you do not have this problem. If the second is a fraction of the first, you have been paying for traffic and letting it go cold overnight.