I am not aware that either of those governments came under Argentine pressure or were challenged about compromising regional solidarity. They took the view, as do most in the region, that it is perfectly possible to have a full and productive bilateral relationship with the UK whilst maintaining a difference of view on the Falklands issue.
Switching support from Argentina to the United Kingdom on the Falkland/Malvinas dispute would make Peru look inconsistent and would not likely result in any diplomatic benefits for Lima in its maritime dispute with Santiago. Chile and the United Kingdom have had strong historical ties going back over a century, and even if Lima were to change its position on the Falkland/Malvinas dispute, there is little chance that London would support Peru in its maritime dispute with Chile. Moreover, that maritime dispute has already moved from the field of diplomatic negotiations (where allies can sometimes play a helpful role) to the realm of judicial adjudication before the ICJ, where cases should be decided on their legal merits.