Each bun is different in terms of how much interaction they want. One of my buns is very needy and wants to be petted and played with all day, but the others are happy to just have a brief petting session each day. I do think it’s important for there to be activity around the bun so they aren’t lonely or bored. Does he get to roam around the house where you spend the most time? If so, then he is getting some stimulation from you being around, even if you aren’t paying 100% attention to him.
I spend most of the day in the same room as one of my pairs bunnies (they are in my bedroom/office), and mine also spend most of that time sleeping! My other pair lives downstairs, and I spend a few hours morning and evening with them (but I’m usually doing things for a chunk of that time, like making dinner, etc.).
Basically you want to plan to spend time with him when he’s most active, so usually morning and evening. Mine tend to be food obsessed before they get their salad, and then after they eat they are more interested in getting some cuddles from me. I’ll usually go give them some pets in the afternoon while they are sleepy as well. I’ve figured out a little routine with them, so I think just experimenting with what times you are hanging out with him will help.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.