Yeah it could well be SE traffic - it's odd why the revenue is varying though, although with this sort of behaviour it could be that the organic SE traffic/rankings are changing as the DNS (and so content, or lack thereof) is changing.
It could be worth developing it a bit. Get a host (if you need a free hosting account temporarily - i.e. a few months - just let me know) who offers cPanel and so AwStats. Have a mini-site (well, a small but good site) developed on it and see how you get on. AwStats is a great tool and will tell you exactly where you are getting your traffic from (be it type-ins, SEs, other websites etc) and if it is SEs, it'll give you the exact keywords being searched for. Could be worth a test because if this traffic is from the SEs, you could perhaps increase your revenue via mini-site development.
As for the temporary jump in revenue/traffic - there is something called the "Google Dance" (a weird name but that's what it's known in SEO circles) which could explain this.
This is basically whereby a new website, or one with very different content (i.e. if you change from Parked to Sedo and then back..) gets a temporary boost in the search engines. You may one day go to the first page of Google for a particular keyword (well, a low competition keyword) and the following day go back down to page three or four. This is whilst Google runs various 'tests' on your site, and whilst your site's rankings propogate throughout their many servers.
Hence it is possible (but I could be wrong) that this is what's happening here - i.e. you change your content, and so Google begins its "dance" of your site. It'll rank it highly, hence the increase in traffic and so revenue. Then over a few days it'll work out where your site should really be ranked (i.e. not on page 1 since parked sites obviously aren't viewed highly by Google) and you'll go to page 3/4+. This then causes the fall in traffic hence revenue.
I could be wrong here. But getting hosting (feel free to PM me for a temporary freebie account) with AwStats on it and a basic website will help you to see where you traffic is coming from and the KWs being searched for it is indeed SE traffic.