Gemini API repeatedly throwing false busy / rate-limit errors in mobile app integration

URGENT: Gemini API 404 + 429 errors in my Android Studio app
I am developing an Android application called FlowSight using Kotlin/Android Studio and the Gemini API.
My app uses Gemini to analyze photographs of electrical schematic diagrams and reconstruct them as editable electrical circuits.
The AI connection has recently become unreliable.
My app reports:
“Google AI brain not found. Please check GEMINI_MODEL_NAME in local.properties.”
Logcat also shows HTTP 404 NOT_FOUND for the configured/fallback Gemini models and HTTP 429 RESOURCE_EXHAUSTED errors.
The app appears to attempt multiple Gemini requests for a single schematic scan, including fallback attempts, and then tells the user to wait several seconds.
I need help determining whether the problem is:
An invalid/deprecated model name,
An incorrect API version or endpoint,
A quota/rate-limit problem,
An API-key/project problem,
Or incorrect fallback/retry logic in my Android code.
I am NOT asking for help redesigning the circuit reconstruction yet. I first need to establish that my Gemini API connection is healthy and that one test request can reliably reach a currently supported model.
I can provide the exact Logcat output, model name, API endpoint/version, and relevant Gemini provider code.
Please tell me exactly which model name, API version, and endpoint I should currently use for this project and how I can verify that the API key can successfully call that model.
I have deliberately omitted my API key from this post.