What are some signs that he's losing interest in me through text messages?

Look at what he is doing, not just how long he takes. A guy who is interested still asks you things. He follows up on something you mentioned two days ago, sends you a link to something you talked about, or starts a new topic on his own. When all of that stops and he only answers what you send, the effort is leaving the conversation. Check whether his messages are getting shorter in a steady way, and whether the gaps between replies are growing even on days when he is clearly free, like the weekend. If he is still responsive on the days he has time, the problem is probably not interest. If he goes quiet on the days he could text and does not, that tells you more than any single sentence he writes. Also notice whether he still refers back to things you have shared. A guy who is losing interest stops building on earlier conversation, so each exchange starts from scratch.

Interest in texting and interest in meeting are different. Some men text casually and only become motivated once a plan is on the table. Others use texting as a way to keep a door open without ever walking through it. The useful test is whether he has ever proposed a specific time, place, or activity. If the conversation has been going for a week and he has never suggested anything concrete, that is information. Pay attention to how he responds when you bring up meeting. Enthusiasm followed by vague follow-through is different from a clear yes that never gets scheduled. A man who wants to see you tends to name a day, and when he does not, you can stop reading the texts for hidden meaning and treat the lack of a plan as the answer.

Give a fade a fair window before you call it. Two or three days of thinner replies is normal and proves very little. A full week of declining effort, with no plan ever proposed, is a reasonable point to draw conclusions. If you send one clear, low-pressure message that gives him an easy opening and he still answers flatly or not at all, you have your answer. At that point the right move is to stop initiating for a while. Let him be the one to restart if he wants to. If he does come back with real energy, you can reassess. If he does not, the silence has told you what you needed to know, and you can put the time and attention into people who are actually showing up.