The Commander looks like a Gruen based on style. But I don’t recognize the movement as being Gruen. There were 6 other outfits that used the Commander name, so it could be one of those. The case was made by Pioneer which was not the name of a watch company.
The Elgin is definitely Swiss. The movement is a Swiss made Font. Calibre 28, not made by Elgin. A very common movement from the 1950s. See image from the Ranfft archive.
The Caravelle movement is a Japanese copy of the Eta 1080 movement. Bulova used this movement a lot in Caravelle and Arday brand watches. see image from the Ranfft archive.
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FHF 28
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Eta 1080
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