I did something similar for a client for a while. I based my proposal on time as others have suggested.
I did: 30 mins a day for researching, reading and scheduling c5 Tweets (Bufferapp is my fave) a day x 5 days. And then I added in 2 hours a month for 'account maintenance' eg following more people, responding to messages (mainly "Thanks for the RT" in my case) and producing a short analytics report. I wasn't writing any original content. Once I got into the swing of it, it probably took a bit less than 30 mins. But you do have to look at content carefully, lots of stuff can be drivel/old.
I didn't enjoy the pressure of having something to do everyday (like you I was back Tweeting on DD's day 2!) and as others have mentioned you need to think about holidays/being with another client all day etc. It is difficult to outsource it for a few days.
However, it is a good way to learn more about the market you are working in and might help with content ideas should you be asked to write the content for them too.
I think it also depends on the business. If it is a kitchen designer, it might just be promo tweets and sharing design content, which can be scheduled. However, something more interactive, a FMCG brand or a charity/organisation that is very PR/newsy then it will need more management.
I think it is fine to go back and ask your client:
- is there a strategy set up?
- has the target audience been defined?
- what sort of engagement are they expecting? What measures will his client be looking for?
- what is the sign off process for tweets - ie is somebody going to check each one or will you be left to it after a bit?
I am guessing he'll have a standard brief for freelancers he uses - ask if he has?
I would stick to the top price you charge him. I get the idea of different rates, but whilst you are Tweeting for him at a lower rate you cannot do other higher rate stuff for other clients. £10 sounds very low, where are you based?
On a related note I was once looking at the idea of outsourcing one of my client's social media and I found a good freelancer who would cover Twitter and Facebook for £350 a month. That was for a high profile issue charity.
I would give it a go, as you say this could be the start of a new package of services you can offer!