We have made radio continuum , H i and X-ray observations in the direction of the unidentified EGRET source 3EG J1410 - 6147 , using the Australia Telescope Compact Array and the Chandra X-ray Observatory . The observations encompass the supernova remnant ( SNR ) G312.4–0.4 and the two young pulsars PSRs J1412–6145 and J1413–6141 . We derive a lower distance limit of 6 kpc to the SNR , although interpretation of positive velocity features in the H i spectrum may imply the SNR is more distant than 14 kpc . PSR J1412–6145 , with an age of 50 kyr , is the pulsar most likely associated with SNR G312.4–0.4 . X-rays are not detected from either pulsar and diffuse X-ray emission near the bright western edge of the SNR is weak . Although there is circumstantial evidence that this western region is a pulsar wind nebula ( PWN ) , the embedded pulsar PSR J1412–6145 is apparently not sufficiently powerful to explain the radio enhancement . The origin of the electron acceleration in this region and of the \gamma -rays remain unidentified , unless the distance to PSR J1413–6141 is at least a factor of 3 lower than its dispersion measure distance .