Does Signal have or plan to have an open source client? Not necessarily freely licensed, just with some minimal auditable component available (like Tarsnap.)

I have no reason not to trust the app, but it would be great if the trust in Signal was strengthened by knowing that (at least) the client source code had been publicly audited and could be verified and built by end users.

Too tin-foil-hatty?

Signal's server[1] and client source code[2,3,4] has been publicly available for many years and are even licensed under the (A)GPL-3.0 (with an exception to allow distribution via Google Play and the Apple App Store).

I don't know where you got the impression this wasn't the case. An earlier VOIP product of theirs (RedPhone) had a proprietary server implementation, but ever since the feature was added to Signal proper it has been free software.

[1]: https://github.com/signalapp/Signal-Server [2]: https://github.com/signalapp/Signal-Android [3]: https://github.com/signalapp/Signal-iOS [4]: https://github.com/signalapp/Signal-Desktop