### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

Closest matches, neither of which covers this: - #24571 reported the same symptom (Proxy, v1.81.9) but was auto-closed as stale/NOT_PLANNED on 2026-07-01 without a fix. This report adds the root cause, both replay channels, and a proposed fix location. - #18160 / PR #18374 fixed signature leakage, but only toward **non-Gemini** targets. The Gemini→Gemini cross-endpoint case is still broken.

### What happened?

We run a LiteLLM `Router` where the primary is a Vertex AI Gemini deployment and the first fallback is the **same model** on Google AI Studio, e.g.:

- primary: `vertex_ai/gemini-3.5-flash` - fallback: `gemini/gemini-3.5-flash`

In multi-turn tool-calling conversations (thinking enabled), whenever the Vertex primary fails mid-conversation (e.g. 429) and the Router falls back to the AI Studio twin, AI Studio rejects the request:

> `GeminiException BadRequestError - code 400, "Corrupted thought signature.", INVALID_ARGUMENT`

Root cause: Gemini thought signatures are **endpoint-bound** — a signature minted by Vertex AI does not validate on `generativelanguag…