Sony DSLR-A390 Instruction Manual page 125

Keeping the LCD monitor tuned on while looking into the
viewfinder
When the LIVE VIEW/OVF switch is set to "OVF," looking into the
viewfinder turns off the LCD monitor.
In the default setting, while looking into the viewfinder, the LCD monitor
is turned off to prevent the battery pack from wearing down.
If you want to turn on the LCD monitor while looking into the viewfinder,
select [Off].
MENU button t 1 t [Auto off w/ VF] t [Off]
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