かべがわ is the only correct reading in your context.
へきそく is a rare reading used in medical contexts to translate parietal pleura (壁側胸膜【へきそくきょうまく】), parietal peritoneum (壁側腹膜【へきそくふくまく】) and so on, but laypeople do not know this reading. (BTW, parietal lobe of the brain is 頭頂葉【とうちょうよう】.) There are several similar terms that end with そく, all of which are almost never used outside medical contexts:
| Word | Ordinary reading | Medical termMedical term |
|---|---|---|
| 頭側 | あたまがわ | とうそく (cranial/superior) |
| 尾側 | - | びそく (caudal/inferior) |
| 右側 | みぎがわ | うそく (right) |
| 左側 | ひだりがわ | さそく (left) |
| 同側 | - | どうそく (ispilateral) |
| 対側 | - | たいそく (contralateral) |
| 片側 | かたがわ | へんそく (unilateral) |
| 両側 | りょうがわ | りょうそく (bilateral) |
| 腹側 | はらがわ | ふくそく (ventral/anterior) |
| 背側 | - | はいそく (dorsal/posterior) |
| 内側 | うちがわ | ないそく (inner/internal; medial) |
| 外側 | そとがわ | がいそく (outer/external; lateral) |
| 口側 | くちがわ | こうそく (oral) |
| 肛側 | - | こうそく (anal) |
I don't know when to read it as かべぎわ. Since the old orthography is used, it may be some obsolete reading. かべぎわ is usually written as 壁際.