Why is 指 repeated twice in 他指了指墙上的画?
I'm surprised this hasn't been covered before here, I'm sure there must be a link somewhere that I was unable to find.
This is the V + 了 + V structure.

#Grammar 2. 动词的重叠 Reduplication of Verbs (II): V了V
Some verbs can be reduplicated in the form V了V structure to indicate that

the action takes only a short amount of time and/or
the action is done only for a limited amount of times
the action has already been done

The V了V structure is usually used for narration.
☑ See also 动词的重叠 Reduplication of Verbs (I): VV and V一V.
For the V了V structure , the verbs are duplicated in the following ways:
单音节词 (Dānyínjí Cí ▸ One-character Verb)

听 - 听了听
想 - 想了想
笑 - 笑了笑

双音节词 (Shuāngyínjí Cí ▸ Two-character Verb)

介绍 - 介绍了介绍
练习 - 练习了练习
休息 - 休息了休息

离合词 (Líhé Cí ▸ Two-character Detachable Compound Verbs)

唱歌 - 唱了唱歌
散步 - 散了散步
游泳 - 游了游泳

Below are example sentences to study Reduplication of Verbs - V了V:
Yéye xiào le xiào, duì wǒ shuō: “Wǒ xiāngxìn nǐ!”
爷爷笑了笑，对我说：“我相信你！”
Grandpa smiled “really quick”, (and) said to me , “I trust you!”
Yè Jīnglǐ tīng le tīng wǒmen de jièshào, méiyǒu shuō bù, yě méiyǒu shuō hǎo.
叶经理听了听我们的介绍，没有说不，也没有说好。
Manager Ye listened to our introduction “really quick”, (they did) not say no, (did) not say yes either.
Nǎinai zuò zài yǐzi shang xiūixi le xiūxi.
奶奶坐在椅子上休息了休息。
Grandma sat on (the) chair (and) rested &quot;really quick&quot;.
Wǒ yǐqián chéngjì bù hǎo, jīnnián nǔ le nǔlì, kǎo de búcuò.
我以前成绩不好，今年努了努力，考得不错。
Before my score (was) not good, this year (I) worked hard “for a little bit”, (I) took (the) test not bad.