Invisible people are bad. They start with good intentions and all that but eventually turn bad. You just have to read H.G Wells.
I have always hated invisible mode feature of IM clients. I understand why people use it but I hate their reasoning nonetheless. So here is my advice, friends don’t stay invisible to friends.
When you stay invisible and ping a person and start a conversation with him/her, you are being rude. The other person had fucking no way of saying something to you, if he had something urgent about which he wanted to talk. If you are actively using the IM client, turn off invisible mode. People aren’t really dying to talk to you, trust me you are not that important, but someone who is important to you – won’t be able to get his/her message across.
If you are busy and rather do not want to be disturbed, just disable notifications. That way, people can still reach you and you will not be bothered. If you can’t help yourself from checking IM window every 2 minutes, just logout. You can also use ‘status’ icon/message for letting people know that, you do not want to be disturbed.
When all else fails, you can block people who are excessively chatty. If he is a friend/colleague you can talk them frankly and set some boundaries.