TL;DR
Rightly or wrongly, project managers are generally measured against the success of their projects and those projects' adherence to a schedule or budget, rather than against a daily breakdown of the PM's allocated time. While every project management framework has an expected percentage of process overhead, this overhead isn't really meaningful in terms of measuring the PM's adherence to a schedule on an individual level. Even if it were possible, it wouldn't be a useful performance indicator for the project management role.
Measuring Project Management
Is it possible to define, in general terms, how PMs allocate their time, over a working day, to key activities such as Meetings with development, Admin and Stakeholder Management? Can these be expressed as percentages of the working day?
If you take a step back, what you're really trying to do here is to define performance indicators or trackable metrics for success as a project manager. However, how much time you spend on particular activities is not how you measure success in the role. Instead, a project manager should be measured by how effectively they control the project (when given sufficient authority to actually do so), or how well they evangelize or communicate about the project within the organization.
Some meaningful measures of project management effectiveness include:
- Communications velocity (e.g. how quickly project information travels through organizational channels).
- Reporting accuracy.
- Transparency of project status.
- Effectiveness at facilitating team and stakeholder meetings.
- Ability to store and retrieve essential project management artifacts.
Some common but hard-to-measure (and therefore potentially less useful) metrics of efficacy may also include:
- Ability to quickly identify projects that are out of tolerance.
- Ability to use influence in roles without sufficient formal authority.
- Ability to collaborate with task performers and stakeholders to mitigate project risks as they are uncovered.
It is often the case that project managers will be praised or blamed for the status of a project, even if they have no actual control over the outcome. However, the best project managers do influence the outcome of projects. They can justifiably take credit for designing and implementing project controls that keep the project within tolerances, or informing management in a timely fashion when a project can't be salvaged.
Communications is really the central key performance indicator for project managers, and communication tasks are where successful project managers spend the majority of their time outside of reporting and other framework-specific ceremonies. If your day isn't filled with communications-related tasks of one sort or another—allowing for sufficient slack to handle interrupt-driven issues, of course—then you're probably not focused on the right things within the role.