In practice, most roles are flexible and can be made to fit the actual skills you bring to the team. However, that usually occurs slowly after you have a position.
The company is expecting one thing from this role, and you another. The 20% development is a deal breaker for you it seems, as the company expects you to be more adept at it than you believe yourself to be. It is worth exploring that with them openly, with the goal of reducing your exposure to actual development and pitching for a more senior position focused on the people management, project management and client-facing parts of the job.
It may be an uphill struggle if the recruiting company reps are set in what they think they need.
The hard part you face is negotiating a change to the role as a candidate as opposed to growing yourself and the role into a matching balance of needs and skills in an existing position. You have a much better chance with a smaller company where the role is covering more ground than with a large company that already has a "Head of Development".
If you think there is space for you to have a role different from the "Senior Technical Lead" role they have open, and you think there is room for flexibility in that company then I suggest contact the company and be honest about your expectations for the role, and try and negotiate a different set of responsibilities. If you have already interviewed with them and declared a 20% development workload is OK, you will need to retract that - it clearly isn't the case for you.
Be prepared to be told "no" because the company has an understanding (right or wrong) about the role it needs already. Also, there is no shame at any stage in walking away from the interview process because it isn't a good fit for you.
At this stage, if the negotiation seems too far fetched an idea then you could still do the test in good faith, and follow up afterwards with comments to the effect that you like the company but doing the test has "enlightened" you that in reality you are looking for a more senior role. Keep that positive, no complaining about the test, just a "thank you" and a pitch for a different role. Maybe in future they will have one available, and it is entirely possible they will need to go through with their idea of senior dev/manager, find it doesn't work as well as they imagined and then post a job which is a better match for you.