Firstly, you could use different methods/frameworks to run projects. Scrum wouldn't necessarily be the solution here as your prime concern is around the line in responsibilities between these two, both different and both required, roles. As well as getting the right level of communication set up.
I have grasped something from the tone of your question that seems to highlight already a problem. In your question you say:
A non-technical PM cannot identify certain dependencies because they have no idea that they exist. Hence my question.
On this note I would strongly recommend you start removing the 'non-technical' attribute to the role. That's not the real problem. The role of the PM is not to work out the technical dependencies by himself/herself but to manage them with the support and expertise of the team involved. If you are the Technical Lead, that's what you are there for. You have the best detailed information about the technical aspects of the project and understand better the dependencies.
Coming back to the separation of duties you could refer to Project Management and Delivery frameworks like DSDM Atern. If you take a look at the DSDM Atern Roles and Responsibilities diagram below you can appreciate that the Project Manager (blue) and Technical Coordinator (green) roles work together towards delivering business value (working along side with Business Sponsor and Visionary).
Some of the responsibilities of the Project Manager in this model would be:
- Communicating with senior management and the project governance
authorities (Business Sponsor, project board, steering committee,
etc.) with the frequency and formality that they deem necessary
- High-level project planning and scheduling, but not detailed task
- Monitoring progress against the baselined project plans
- Managing risk and any issues as they arise, escalating to senior
business or technical roles as required
- Managing the overall configuration of the project Motivating the teams to meet their
- Managing business involvement within the Solution Development Teams
- Resourcing Specialist Roles as required Handling
problems escalated from the Solution Development Teams
- Coaching the Solution Development Teams when handling difficult situations
While for the Technical Coordinator:
- Agreeing and controlling the technical architecture
- Determining the technical environments
- Advising on and co-ordinating each team’s technical activities
- Identifying and owning architectural and other technically based
risk, escalating to the Project Manager as appropriate
- Ensuring the non-functional requirements are achievable and
- Ensuring adherence to appropriate standards of technical best
- Controlling the technical configuration of the solution
- Managing technical aspects of the transition of the solution into
- Resolving technical differences between technical team members
The combination of the two roles is really powerful and usually leads to project success.
Now, we need to address the communication problem.
I always say to people they need to stop waiting for things to happen and point the finger later if things didn't work out the way they expected. This behaviour helps nobody.
If the Project Manager in your team has not come forward to work with you on how regularly you guys should meet or the tools to report please feel more than empowered to start that conversation yourself.
You mentioned that you are already using Jira so maybe you two could sit together a couple of hours to determine the best way to use the functionality to capture technical dependencies - linking issues from different projects back to a "Dependencies" project list- report status, and advise whether there is a team already looking at the issue, etc...
I have personally used Jira with GreenHopper for similar reports and it has worked very well.