Open versus Closed: Personality, Identity, and the Politics of Redistribution (Johnston, Lavine, & Federico, 2017) is a good reference that talks about how political engagement relates to psychology. Includes review of literature in this area.
More specifically, research is covered that explores the role political figures have in informing what Americans want from the government, and how individual difference in psychology contribute to this.
They find that for politically active citizens these attitudes are not driven by self-interest, but by a desire to express the traits and cultural commitments that define their identities.
This book is a great general reference that speaks to the dynamic between those that are politically engaged and elected officials.
More specific to your question, Sherman et al. (2020) examines communication in the exchange between citizens and elected officials on climate policy. Sample was drawn by
...recruiting citizen activists who lobby the US Congress for a carbon pricing policy to address climate change (Sherman et al., 2020, p.576).
In this way, 4 social psychological approaches including: affirmation, social norms, legacy and immediacy, were examined to assess how citizens think about and contact political leaders. Sherman's et al (2020) results show:
A strategy of establishing shared values and common ground (affirmation) was used most frequently overall. While, emphasizing the long-term costs and benefits of addressing climate change (legacy) was employed less frequently than affirmation and seen as less effective by activists, but it was the only strategy that was associated with perceived increases in Congressional Representatives’ support of the policy.
Johnston, C., Lavine, H., & Federico, C. (2017). Open versus Closed: Personality, Identity, and the Politics of Redistribution. Cambridge: Cambridge University Press. doi: 10.1017/9781316341452
Sherman, D., Shteyn, M., Han, H., & Van Boven, L. (2021). The exchange between citizens and elected officials: A social psychological framework for citizen climate activists. Behavioural Public Policy, 5(4), 576-605. doi: 10.1017/bpp.2020.41